A volute design method considering the influence of the volute tongue

Abstract

The present invention discloses a volute design method considering the influence of the volute tongue, which includes: giving the velocity boundary of the volute at the volute tongue, including the radial velocity and the tangential velocity, and being circumferentially uniform; considering the influence of the volute tongue, and in order to satisfy the conservation of angular momentum, only adjusting the radial velocity distribution, controlling the circumferential variation of the radial velocity through a function, increasing at the volute tongue, and then decreasing gradually after the volute tongue and recovering to the initial value; designing the volute according to the new velocity boundary through the existing two-dimensional design method to generate a three-dimensional geometric volute model. The design method proposed by the present invention considers the influence of the volute tongue on the flow parameters, obtains a more reasonable volute A / R curve by changing the flow distribution before and after the volute tongue during design, makes the flow parameters at the rotor inlet downstream of the volute more uniform, significantly reduces the excitation force received by the rotor, prevents the rotor from occurring high-cycle fatigue, and prolongs the service life.

Description

Technical Field

[0001] The present invention relates to the field of radial flow turbomachinery, and particularly to a volute design method considering the influence of the volute tongue. Background Art

[0002] Radial flow turbomachinery is widely used in social production and life, such as common centrifugal compressors, centrifugal pumps, centrifugal fans, centripetal turbines, and some hydraulic turbines, etc. The most important components of radial flow turbomachinery are the rotor and the volute. The volute plays a role in circumferentially collecting fluid and diffusing fluid in centrifugal turbomachinery, and plays a role in distributing fluid and accelerating fluid in centripetal turbomachinery. The design level of the volute will directly affect various indicators such as the working efficiency, reliability, vibration, and noise level of radial flow turbomachinery. At present, the design level of radial flow turbomachinery has encountered a bottleneck, and it is difficult to achieve a significant improvement in performance. In particular, the design level of the volute is relatively backward compared with the rotor, which hinders the improvement of the overall performance of radial flow turbomachinery.

[0003] Existing design methods for centripetal turbine volutes include one-dimensional methods and two-dimensional methods. Both of these methods assume that the mass flow rate or velocity at the volute outlet is circumferentially uniformly distributed, ignoring the circumferential non-uniformity caused by the volute tongue, increasing the non-uniformity degree of the flow parameters at the rotor inlet downstream of the volute, resulting in the rotor being more prone to high-cycle fatigue and reducing the service life. Summary of the Invention

[0004] The present invention provides a volute design method considering the influence of the volute tongue to weaken the influence of the volute tongue on the flow parameters at the rotor inlet, prevent the occurrence of high-cycle fatigue of the rotor blades, and extend the service life of the turbine.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A volute design method considering the influence of the volute tongue, comprising the following steps:

[0007] Step 1, give the velocity boundary of the to-be-designed volute at the volute tongue, including the radial velocity and the tangential velocity, and set the initial values of the radial velocity and the tangential velocity to remain unchanged in the circumferential direction;

[0008] Step 2, set three azimuth inflection points within the range of azimuth angle from 0 to 2π, divide it into four azimuth angle intervals, keep the tangential velocity unchanged, and adjust the radial velocity at azimuth angles of 0, 2π, and the three azimuth inflection points;

[0009] The adjustment scheme of the radial velocity is as follows:

[0010] At the azimuth angle of 0, increase the initial radial velocity as the first boundary radial velocity;

[0011] At the first inflection point of the azimuth angle, reduce the initial radial velocity as the second boundary radial velocity;

[0012] At the second inflection point of the azimuth angle, keep the initial radial velocity unchanged as the third boundary radial velocity;

[0013] At the third inflection point of the azimuth angle, keep the initial radial velocity unchanged as the fourth boundary radial velocity;

[0014] At the azimuth angle of 2π, increase the initial radial velocity as the fifth boundary radial velocity;

[0015] Step 3: According to the three azimuth angle inflection points and the adjusted five boundary radial velocities, create an interval piecewise function between the radial velocity and the azimuth angle in the four azimuth angle intervals respectively;

[0016] The creation scheme of the piecewise function is as follows:

[0017] Create the first interval piecewise function between the azimuth angle of 0 and the first inflection point;

[0018] Create the second interval piecewise function between the azimuth angle of the first inflection point and the second inflection point;

[0019] Create the third interval piecewise function between the azimuth angle of the second inflection point and the third inflection point;

[0020] Create the fourth interval piecewise function between the azimuth angle of the third inflection point and 2π;

[0021] Step 4: Take the adjusted five boundary radial velocities and the four interval piecewise functions as the new velocity boundary conditions;

[0022] Step 5: Design the volute according to the new velocity boundary conditions to generate the three-dimensional geometry of the volute.

[0023] Further, the value range of the three azimuth angle inflection points in step 2 includes:

[0024] The first azimuth angle inflection point θ1 is 15 to 20 degrees;

[0025] The second azimuth angle inflection point θ2 is 50 to 60 degrees;

[0026] The third azimuth angle inflection point θ3 is 345 to 350 degrees.

[0027] Further, the numerical range of changing the boundary radial velocity in step 2 includes:

[0028] At the azimuth angle of 0, the boundary radial velocity is 1 to 2 times the initial radial velocity;

[0029] At the first inflection point of the azimuth angle, the boundary radial velocity is 0.5 to 1 times the initial radial velocity;

[0030] At the second inflection point of the azimuth angle, the boundary radial velocity is equal to the initial radial velocity;

[0031] At the third inflection point of the azimuth angle, the boundary radial velocity is equal to the initial radial velocity;

[0032] At the azimuth angle of 2π, the boundary radial velocity is 1 to 2 times the initial radial velocity.

[0033] Furthermore, the piecewise function used in step 3 includes a linear function:

[0034] Radial velocity in the azimuth angle range of 0 to θ1:

[0035]

[0036] Radial velocity in the azimuth angle range of θ1 to θ2:

[0037]

[0038] Radial velocity in the azimuth angle range of θ2 to θ3:

[0039] V3 = V r ;

[0040] Radial velocity in the azimuth angle range of θ3 to 2π:

[0041]

[0042] Where: θ is the azimuth angle independent variable; θ1, θ2, and θ3 are the first inflection point, the second inflection point, and the third inflection point of the azimuth angle respectively; is the boundary radial velocity at the azimuth angle of 0, is the boundary radial velocity at the azimuth angle θ1, is the boundary radial velocity at the azimuth angle of 2π; V r is the initial radial velocity.

[0043] Furthermore, the piecewise function used in step 3 also includes a power function:

[0044] Radial velocity in the azimuth angle range from 0 to :

[0045]

[0046] Radial velocity in the azimuth angle range from to θ1:

[0047]

[0048] Radial velocity when the azimuth range is θ1 to θ2:

[0049]

[0050] Radial velocity when the azimuth range is θ2 to θ3:

[0051] V4 = V r ;

[0052] Radial velocity when the azimuth range is θ3 to 2π:

[0053]

[0054] Where: θ is the azimuth independent variable; θ1, θ2, and θ3 are the first inflection point, the second inflection point, and the third inflection point of the azimuth respectively; is the boundary radial velocity when the azimuth is 0, is the boundary radial velocity at azimuth θ1, is the boundary radial velocity when the azimuth is 2π; V r is the initial radial velocity.

[0055] Furthermore, the piecewise function used in step 3 further includes trigonometric functions:

[0056] Radial velocity when the azimuth range is 0 to θ1:

[0057]

[0058] Radial velocity when the azimuth range is θ1 to θ2:

[0059]

[0060] Radial velocity when the azimuth range is θ2 to θ3:

[0061] V3 = V r ;

[0062] Radial velocity when the azimuth range is θ3 to 2π:

[0063]

[0064] Where: θ is the azimuth independent variable; θ1, θ2, and θ3 are the first inflection point, the second inflection point, and the third inflection point of the azimuth respectively; is the boundary radial velocity when the azimuth is 0, is the boundary radial velocity at azimuth θ1, is the boundary radial velocity when the azimuth is 2π; V r is the initial radial velocity.

[0065] Beneficial effects: The present invention relates to a volute design method considering the influence of the volute tongue. By considering the influence of the volute tongue on the air flow parameters on the basis of the existing two-dimensional design method, the radial velocity distribution before and after the volute tongue is changed, so that the air flow parameters are more uniform, preventing the rotor from suffering from high-cycle fatigue and improving the service life of the turbine. Brief Description of the Drawings

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0067] Figure 1 It is a schematic diagram of one-dimensional volute design in the prior art;

[0068] Figure 2 It is a schematic diagram of the circumferential distribution of A / R of the volute in the two-dimensional volute design method in the prior art;

[0069] Figure 3 It is a circumferential distribution diagram of the air flow angle at the outlet of a certain volute designed by the two-dimensional method in the prior art;

[0070] Figure 4 It is a flow chart of the volute design method considering the influence of the volute tongue disclosed by the present invention;

[0071] Figure 5 It is a circumferential distribution diagram of the radial velocity using the method disclosed by the present invention;

[0072] Figure 6 It is a comparative diagram of the circumferential distribution of A / R of the volute designed by the two methods;

[0073] Figure 6a It is a comparative diagram of the circumferential distribution of A / R from azimuth angle 0 to 90 degrees;

[0074] Figure 6b It is a comparative diagram of the circumferential distribution of A / R from azimuth angle 300 degrees to 360 degrees;

[0075] Figure 7a It is a schematic diagram of 100 volute cross-sections created using the prior art;

[0076] Figure 7b It is a schematic diagram of 100 volute cross-sections created using the method of the present invention;

[0077] Figure 8 It is a comparative diagram of the circumferential distribution of the air flow angle at the outlet of the volute of the two methods without the impeller;

[0078] Figure 9Comparison diagram of the circumferential distribution of the volute outlet airflow angle for two methods in the case of having an impeller. Specific implementation mode

[0079] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts fall within the scope of protection of the present invention.

[0080] Existing centripetal turbine volute design methods include one-dimensional design methods and two-dimensional design methods. As Figure 1 shown, the one-dimensional volute design method only considers the flow of the working fluid along the centroid of the volute cross-section during the design process. The solid black arrow indicates the flow direction of the working fluid. In the figure, A is the cross-sectional area of a certain part of the volute, and R is the radius of the centroid of the volute cross-section. By assuming a circumferentially uniform distribution of the mass flow rate at the volute outlet and the conservation of angular momentum, the relationship between the ratio A / R of the volute cross-sectional area A to the cross-sectional centroid radius R and the azimuth angle θ can be determined. However, the one-dimensional method can only obtain a linear A / R distribution curve and cannot determine the shape of the volute cross-section.

[0081] The two-dimensional design method of the centripetal turbine volute can directly generate a three-dimensional volute model based on basic equations such as mass conservation, energy conservation, angular momentum conservation, and streamline equations, and considering the axial width of the volute. Similar to the one-dimensional method, the two-dimensional method also assumes a circumferentially uniform distribution of the mass flow rate or velocity at the volute outlet. However, since the change in the density of the working fluid is considered during the solution, a slightly convex A / R curve will be obtained at this time, as Figure 2 shown.

[0082] In the one-dimensional method and the two-dimensional method, it is assumed that the mass flow rate at the volute outlet is circumferentially uniform. One is to simplify the design, and the other is to make the flow parameters at the volute outlet uniform to reduce the excitation force on the rotor downstream of the volute. However, this assumption ignores the influence of the volute tongue, and the designed volute cannot achieve the expected effect. Taking the two-dimensional design method as an example, in the case of no impeller, a three-dimensional CFD simulation calculation is performed on the volute described in Figure 2 to obtain the circumferential distribution diagram of the airflow angle at the volute outlet position with respect to the azimuth angle, as Figure 3 shown. When the azimuth angle is before 2π, that is, near the volute tongue, the airflow angle increases rapidly. However, after passing through the volute tongue, the airflow angle drops sharply. This phenomenon will cause severe fluctuations in the airflow parameters at the turbine rotor inlet, increase the excitation force on the blades, and easily lead to high-cycle fatigue of the blades.

[0083] Embodiment 1

[0084] This embodiment provides a volute design method considering the influence of the volute tongue, as Figure 4 shown, including the following steps:

[0085] Step 1: Give the velocity boundaries at the volute tongue of the to-be-designed volute, including the radial velocity and the tangential velocity, and set the initial values of the radial velocity and the tangential velocity to remain unchanged in the circumferential direction;

[0086] Step 2: Set three azimuth inflection points within the range of azimuth angles from 0 to 2π, divide them into four azimuth intervals, keep the tangential velocity unchanged, and adjust the radial velocities at azimuth angles of 0, 2π, and the three azimuth inflection points;

[0087] The adjustment scheme of the radial velocity is as follows:

[0088] At the azimuth angle of 0, increase the initial radial velocity as the first boundary radial velocity;

[0089] At the azimuth angle of the first inflection point, decrease the initial radial velocity as the second boundary radial velocity;

[0090] At the azimuth angle of the second inflection point, keep the initial radial velocity unchanged as the third boundary radial velocity;

[0091] At the azimuth angle of the third inflection point, keep the initial radial velocity unchanged as the fourth boundary radial velocity;

[0092] At the azimuth angle of 2π, increase the initial radial velocity as the fifth boundary radial velocity;

[0093] Step 3: According to the three azimuth inflection points and the adjusted five boundary radial velocities, create interval piecewise functions between the radial velocity and the azimuth angle in the four azimuth intervals respectively;

[0094] The creation scheme of the piecewise function is as follows:

[0095] Between the azimuth angle of 0 and the first inflection point, create the first interval piecewise function;

[0096] Between the azimuth angle of the first inflection point and the second inflection point, create the second interval piecewise function;

[0097] Between the azimuth angle of the second inflection point and the third inflection point, create the third interval piecewise function;

[0098] Between the azimuth angle of the third inflection point and 2π, create the fourth interval piecewise function;

[0099] Step 4: Take the adjusted five boundary radial velocities and the four interval piecewise functions as the new velocity boundary conditions;

[0100] Step 5: Design the volute according to the new velocity boundary conditions and generate the three-dimensional geometry of the volute.

[0101] In this embodiment, the value ranges of the three azimuth inflection points include:

[0102] The first azimuth inflection point θ1 is 15 to 20 degrees;

[0103] The second azimuth inflection point θ2 is 50 to 60 degrees;

[0104] The third azimuth inflection point θ3 is 345 to 350 degrees.

[0105] In this embodiment, the numerical ranges of the boundary radial velocity after change include:

[0106] At the azimuth of 0, the boundary radial velocity is 1 to 2 times the initial radial velocity;

[0107] At the azimuth of the first inflection point, the boundary radial velocity is 0.5 to 1 times the initial radial velocity;

[0108] At the azimuth of the second inflection point, the boundary radial velocity is equal to the initial radial velocity;

[0109] At the azimuth of the third inflection point, the boundary radial velocity is equal to the initial radial velocity;

[0110] At the azimuth of 2π, the boundary radial velocity is 1 to 2 times the initial radial velocity.

[0111] Specifically, in the first attempt, the three azimuth inflection points can first take the maximum values and then be adjusted according to the actual situation. Considering the influence of the volute tongue on the rotor inlet air flow parameters, changing the initial value of the radial velocity before and after the volute tongue can effectively weaken the severity of the change of the air flow angle with the azimuth.

[0112] In this embodiment, the specific functional equations for adjusting the radial velocity include but are not limited to the following schemes:

[0113] (1) Linear function:

[0114] Radial velocity in the azimuth range of 0 to θ1:

[0115]

[0116] Radial velocity in the azimuth range of θ1 to θ2:

[0117]

[0118] Radial velocity in the azimuth range of θ2 to θ3:

[0119] V3 = V r ;

[0120] Radial velocity when the azimuth range is from θ3 to 2π:

[0121]

[0122] (2) Power function:

[0123] Radial velocity when the azimuth range is from 0 to :

[0124]

[0125] Radial velocity when the azimuth range is from to θ1:

[0126]

[0127] Radial velocity when the azimuth range is from θ1 to θ2:

[0128]

[0129] Radial velocity when the azimuth range is from θ2 to θ3:

[0130] V4 = V r ;

[0131] Radial velocity when the azimuth range is from θ3 to 2π:

[0132]

[0133] (3) Trigonometric function:

[0134] Radial velocity when the azimuth range is from 0 to θ1:

[0135]

[0136] Radial velocity when the azimuth range is from θ1 to θ2:

[0137]

[0138] Radial velocity when the azimuth range is from θ2 to θ3:

[0139] V3 = V r ;

[0140] Radial velocity when the azimuth range is from θ3 to 2π:

[0141]

[0142] Where: θ is the azimuth independent variable; θ1, θ2, and θ3 are the first inflection point, the second inflection point, and the third inflection point of the azimuth respectively; is the boundary radial velocity at azimuth angle of 0, is the boundary radial velocity at azimuth angle θ1, is the boundary radial velocity at azimuth angle of 2π; V r is the initial radial velocity.

[0143] In this embodiment, all the listed function categories and specific forms can be used in combination during the specific design process. Moreover, there are numerous function forms that can achieve the increasing and decreasing functions of the radial velocity. The above function forms are only used to illustrate the technical solution of the present invention and are not intended to limit it. The specific type or form of the function can be adjusted and modified according to different actual situations during the design process.

[0144] Embodiment 2

[0145] In this embodiment, a preferred case of the technical solution of the present invention is given:

[0146] Adjust the radial velocity, and the parameter settings are as follows:

[0147] The three azimuth angle inflection points are respectively: θ1 = 20°, θ2 = 60°, θ3 = 350°;

[0148] The boundary radial velocity at azimuth angle of 0

[0149] The boundary radial velocity at azimuth angle θ1

[0150] The boundary radial velocity at azimuth angle of 2π

[0151] In this embodiment, the function equation used is:

[0152] When the azimuth angle is in the range of 0 to θ1, a trigonometric function is used to obtain the change curve of the radial velocity, and the formula is as follows:

[0153]

[0154] When the azimuth angle is in the range of θ1 to θ2, a power function is used to obtain the change curve of the radial velocity, and the formula is as follows:

[0155]

[0156] When the azimuth angle is in the range of θ2 to θ3, the radial velocity is constant, that is:

[0157] V3 = V r ;

[0158] When the azimuth angle is in the range of θ3 to 2π, a power function is used to obtain the change curve of the radial velocity, and the formula is as follows:

[0159]

[0160] The above functional equations for each section are the selected solutions proposed by the present invention. Substitute the set parameters into the above four-piece piecewise function. At this time, the set initial radial velocity is a dimensionless parameter, that is, V r = 1; as Figure 5 shown, the schematic diagram of the circumferential distribution of the radial velocity is obtained.

[0161] Specifically, according to the above velocity boundary conditions, a volute is designed to obtain the A / R curve of the volute, as Figure 6 shown. The maximum and minimum A / R of the two volutes are the same. As Figure 6a and Figure 6b shown, compared with the volute designed by the original method, the A / R curve of the volute designed by the present invention will decrease relatively rapidly at the beginning, then change uniformly, and finally decrease relatively rapidly again before 2π, that is, compared with the original method, the A / R curve of the present invention changes more rapidly at both ends, and this change comes from the change of the radial velocity boundary conditions.

[0162] Specifically, in this embodiment, as Figure 7a and Figure 7b shown, they are the cross-sectional views of the volutes generated by the two methods. Figure 7a and Figure 7b The azimuth angles corresponding to the cross-sections in are the same. Figure 7a is a schematic diagram of 100 cross-sections of the volute created using the prior art, that is, the radial velocity remains unchanged within the range from 0 to 2π; Figure 7b is a schematic diagram of 100 cross-sections of the volute created using the method of the present invention. Among them, the largest and smallest cross-sections change faster, which is consistent with the A / R curve.

[0163] Specifically, in this embodiment, in order to test the effect of the new volute, the angular distribution of the air flow of the two volutes is compared. As Figure 8 shown, it is the circumferential distribution of the air flow angle at the outlet of the two volutes without an impeller. It can be seen from the figure that the jump of the volute designed by the present invention before and after the volute tongue is significantly reduced. Among them, the maximum reduction of the air flow angle is about 4°, and the minimum reduction of the air flow angle is about 2°. Therefore, the jump amount before and after the volute tongue is reduced by about 2°.

[0164] Specifically, in this embodiment, in order to more accurately compare the change of the air flow angle, the comparison of the air flow angle at the outlet of the volute is further carried out in the case of having an impeller. As Figure 9As shown, it is the steady-state calculation result under a certain working condition. The airflow angle increases at both the volute tongue and the blade. This turbine has a total of 11 blades. Through comparison, it is found that the flow angle of the volute designed by the present invention fluctuates up and down by about 12° before and after the volute tongue, while that of the original method is 17°, that is, the fluctuation is reduced by about 5°.

[0165] In specific implementation, the values of the azimuth angle inflection point, the initial radial velocity, and the boundary radial velocity can be adjusted according to different actual situations, so that the working fluid flow parameters before and after the volute tongue are more stable, that is, the working fluid flow state at the rotor inlet is more uniform, which can reduce the excitation force on the rotor, reduce the occurrence of high-cycle fatigue, and improve the service life and working efficiency of the turbine.

[0166] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A volute design method considering the influence of the volute tongue, characterized in that It includes the following steps: Step 1: Give the velocity boundaries at the volute tongue of the to-be-designed volute, including the radial velocity and the tangential velocity, and set the initial values of the radial velocity and the tangential velocity to remain unchanged in the circumferential direction; Step 2: Set three azimuth inflection points within the range of azimuth from 0 to 2π, divide it into four azimuth intervals, keep the tangential velocity unchanged, and adjust the radial velocities at azimuths of 0, 2π, and the three azimuth inflection points; The adjustment scheme of the radial velocity is as follows: At azimuth 0, increase the initial radial velocity as the first boundary radial velocity; At the first azimuth inflection point, decrease the initial radial velocity as the second boundary radial velocity; At the second azimuth inflection point, keep the initial radial velocity unchanged as the third boundary radial velocity; At the third azimuth inflection point, keep the initial radial velocity unchanged as the fourth boundary radial velocity; At azimuth 2π, increase the initial radial velocity as the fifth boundary radial velocity; Step 3: According to the three azimuth inflection points and the adjusted five boundary radial velocities, create piecewise functions between the radial velocity and the azimuth within the four azimuth intervals respectively; The creation scheme of the piecewise function is as follows: Create the first interval piecewise function between azimuth 0 and the first inflection point; Create the second interval piecewise function between the first inflection point and the second inflection point; Create the third interval piecewise function between the second inflection point and the third inflection point; Create the fourth interval piecewise function between the third inflection point and 2π; Step 4: Take the adjusted five boundary radial velocities and the four interval piecewise functions as the new velocity boundary conditions; Step 5: Design the volute according to the new velocity boundary conditions to generate the 3D geometry of the volute.

2. The design method of a volute considering the influence of the volute tongue according to claim 1, characterized in that The value range of the three azimuth inflection points in Step 2 includes: The first azimuth inflection point θ1 is 15 to 20 degrees; The second azimuth inflection point θ2 is 50 to 60 degrees; The third azimuth inflection point θ3 is 345 to 350 degrees.

3. A volute design method considering the influence of the volute tongue according to claim 1, characterized in that The numerical range of changing the boundary radial velocity in Step 2 includes: At azimuth 0, the boundary radial velocity is 1 to 2 times the initial radial velocity; At the first azimuth inflection point, the boundary radial velocity is 0.5 to 1 times the initial radial velocity; At the second azimuth inflection point, the boundary radial velocity is equal to the initial radial velocity; At the third azimuth inflection point, the boundary radial velocity is equal to the initial radial velocity; At azimuth 2π, the boundary radial velocity is 1 to 2 times the initial radial velocity.

4. A volute design method considering the influence of the volute tongue according to claim 1, characterized in that The piecewise functions used in Step 3 include linear functions: The radial velocity in the azimuth range of 0~θ1: The radial velocity in the azimuth range of θ1~θ2: The radial velocity in the azimuth range of θ2~θ3: V3 = V r ; The radial velocity in the azimuth range of θ3~2π: Where: θ is the azimuth independent variable; θ1, θ2, and θ3 are the first, second, and third inflection points of the azimuth, respectively; is the boundary radial velocity at azimuth 0, is the boundary radial velocity at azimuth θ1, is the boundary radial velocity at azimuth 2π; V r is the initial radial velocity.

5. A volute design method considering the influence of the volute tongue according to claim 1, characterized in that, The piecewise functions used in Step 3 also include power functions: Azimuth range is from 0 to Radial velocity at this time: Azimuth range is to the radial velocity at θ1: The radial velocity in the azimuth range of θ1~θ2: The radial velocity in the azimuth range of θ2~θ3: V4 = V r ; The radial velocity in the azimuth range of θ3~2π: Where: θ is the azimuth independent variable; θ1, θ2, and θ3 are the first, second, and third inflection points of the azimuth, respectively; is the boundary radial velocity at azimuth 0, is the boundary radial velocity at azimuth θ1, is the boundary radial velocity at azimuth 2π; V r is the initial radial velocity.

6. A volute design method considering the influence of the volute tongue according to claim 1, characterized in that The piecewise functions used in Step 3 also include trigonometric functions: The radial velocity in the azimuth range from 0 to θ1: Radial velocity when the azimuth range is θ1 to θ2: Radial velocity when the azimuth range is θ2 to θ3: V3 = V r ; Radial velocity when the azimuth range is θ3 to 2π: Where: θ is the azimuth independent variable; θ1, θ2, and θ3 are the first, second, and third inflection points of the azimuth respectively; is the boundary radial velocity at azimuth 0, is the boundary radial velocity at azimuth θ1, is the boundary radial velocity at azimuth 2π; V r is the initial radial velocity.

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