A design method for the working wheel of a cryogenic turbine expander

Abstract

This invention relates to a design method for a working impeller of a cryogenic turbine expander, comprising the following steps: obtaining the meridional profile of the working impeller through a graphical method, thereby obtaining the (z, r) cylindrical coordinates of each point on the hub line and the wheel cover line; then calculating the (z, r) cylindrical coordinates of the central streamline; using these as input conditions for the central streamline method to obtain the length of the central meridional streamline and the value of its characteristic function; calculating the θ coordinates of the central meridional streamline in reverse, thereby obtaining the θ coordinates of the hub line and the wheel cover line, thus obtaining the central flow surface of the working impeller blade; finally, obtaining the three-dimensional shape design of the working impeller through a rotational array; this invention combines the graphical method with the central streamline method, which not only improves the problem of the non-smooth and continuous blade flow channel surface in the transition area between the parabolic working impeller guide section and the straight blade section in previous design methods, thus improving the operating efficiency of the turbine expander; but also improves the problem of diameter expansion at the trailing edge of the blade in the central streamline method, facilitating the actual installation of the working impeller.

Description

Technical Field

[0001] This invention relates to the field of cryogenic turbine expander technology, and in particular to a design method for a cryogenic turbine expander impeller. Background Technology

[0002] As a primary refrigeration component, the cryogenic turbine expander is a core element in most cryogenic refrigeration systems. Its stability and operating efficiency significantly impact the overall system's energy consumption and efficiency. Due to its wide range of applications, more and more researchers have devoted themselves to related studies in recent years. Numerous monographs have also discussed in detail the basic concepts and design methods of turbine expanders. Because of the low inlet medium temperature and large expansion ratio, especially at low flow rates, the impeller diameter is small, resulting in a large specific enthalpy drop in the expander. To achieve high adiabatic efficiency, a high rotor speed is inevitable. Therefore, small size and high speed are the obvious characteristics of cryogenic turbine expanders. Currently, there is no universally accepted standard for the theory and design methods of cryogenic turbine expanders. Previous design methods suffer from the problem of uneven and discontinuous blade flow channel surfaces in the transition area between the impeller guide section and the straight blade section.

[0003] Based on Wu Zhonghua's concept of three-dimensional flow in turbine machinery, Hasselgruber proposed a calculation method for designing the blade profile of rotating machinery impellers. This method obtains the cylindrical coordinate parameters of the central streamline from the impeller's inlet leading edge to its outlet trailing edge through characteristic functions. Then, the meridional profile of the impeller is obtained from the geometric relationship between the central streamline, the hub line, and the wheel arch line. Finally, the blade shape is completed based on the angle values ​​of the cylindrical coordinate parameters and the meridional profile. The entire process adjusts the output result through free parameters in the characteristic functions. Because this method considers both the geometric factors of the blade shape and the relative flow characteristics of the fluid in the impeller, it has been widely used. However, the meridional profile obtained using this method is "trumpet-shaped," and the expansion of the diameter at the blade trailing edge makes it unsuitable for complete machine installation when applying this method to the impeller design of turbine expanders. Summary of the Invention

[0004] One objective of this invention is to provide a design method for the working wheel of a low-temperature turbine expander. This method not only improves upon the problem of uneven and continuous blade flow channel surface in the transition area between the parabolic working wheel guide section and the straight blade section in previous design methods, but also facilitates the actual installation of the working wheel, providing a new approach for the design of working wheels for future turbine expanders.

[0005] This invention provides a design method for the working impeller of a cryogenic turbine expander, comprising the following steps:

[0006] S1. Obtain the meridional profile of the working wheel of the low-temperature turbine expander by drawing a graph. Based on the coordinates of the control points of the meridional profile, obtain the cylindrical coordinate values ​​of each point on the hub line and the wheel cover line respectively.

[0007] S2. Calculate the cylindrical coordinate value of the center streamline based on the cylindrical coordinate values ​​of each point on the hub line and wheel arch line;

[0008] S3. Using the cylindrical coordinates of the central streamline as the input condition for the central streamline method, the length of the central meridional streamline and the value of the characteristic function are calculated using the central streamline method.

[0009] S4. Based on the length of the central meridian streamline and the value of the characteristic function, the θ coordinate of the central meridian streamline is calculated, and the θ coordinates of the hub line and the wheel cover line can be obtained, thus obtaining the central flow surface of the working wheel blade.

[0010] In one embodiment of the present invention, step S1 includes the following steps:

[0011] Take the axial length of the working wheel

[0012] B z =(0.3-0.4)D1 (1)

[0013] For the hub profile:

[0014] B z1 =B z (2)

[0015]

[0016] For the shroud profile:

[0017] B z2 =B z -L1 (4)

[0018]

[0019] In the above formula, B z1 B z2 These are the axial lengths of the meridional hub profile and the meridional wheel arch profile, respectively, L. r1 L r2 These are the radial lengths of the meridional hub profile and the meridional shroud profile, respectively. D1 is the diameter of the leading edge of the impeller inlet, D'2 is the diameter of the trailing edge of the impeller outlet shroud, D”2 is the diameter of the trailing edge of the impeller outlet hub, and L1 is the blade height of the leading edge of the impeller inlet.

[0020] Taking the meridional hub profile as an example, the axial length B of the meridional hub profile... z1 Its radial length L r1If the difference is divided into M equal parts, then the length of each part is:

[0021]

[0022] Based on M equal parts, with axial length B respectively z1 With radial length L r1 The intersection points O0, O1, ..., O M Centered on a circle with a radial length L r1 Draw a circle with radius B, and obtain the arc and axial length B respectively. z1 Intersects at points 0, 1, ..., N, where N = M, then the axial length B z1 With radial length L r1 The included angle is also divided into M equal parts, and the angle bisector intersects the corresponding arcs at points P0, P1, ..., P2. N These are the control points for the hub profile of the meridional plane;

[0023] Therefore, the control point P of the meridional hub profile is obtained. N The coordinate expression for (N = 0, 1, ..., M) is P(z N r N ),in,

[0024] z N =B z -(MN)aL r cos(δ N +θ N (7)

[0025]

[0026] In the above formula, z N It is the axial cylindrical coordinate value of the control point, r N It is the radial cylindrical coordinate value of the control point, δ N It is the longer side B z1 With the short side L r1 The angle value θ after dividing the included angle M into equal parts N It is the center and control point P N The angle between the line connecting the two points and the axial direction;

[0027] Combining the Law of Cosines, equations (7) and (8) are transformed into:

[0028]

[0029]

[0030] The calculation methods for the cylindrical coordinate values ​​of the meridional wheel cover profile and the meridional wheel hub profile are the same. The wheel hub profile and wheel cover profile obtained from the control point coordinates of the meridional wheel cover profile and the meridional wheel hub profile are the meridional profiles for designing the turbine expander working wheel.

[0031] In one embodiment of the present invention, in step S1, the value of M ranges from 30 to 50.

[0032] In one embodiment of the present invention, step S2 includes the following steps:

[0033] Based on the meridional coordinate s, establish the geometric relationship between the cylindrical coordinate system (z, r, θ) and the body-fitted orthogonal coordinate system (t, b, n): where the coordinate z is the axial direction of the cylindrical coordinate system, r is the radial direction of the cylindrical coordinate system, and θ is the circumferential direction of the cylindrical coordinate system; the coordinate t is the streamline direction at the center of the flow channel, the coordinate b is the width direction between the pressure surface and the suction surface of the flow channel, and the coordinate n is the depth direction of the flow channel, wherein the meridional coordinate s lies in the zr plane of the cylindrical coordinate system (z, r, θ);

[0034] Based on the geometric relationship between the meridional plane profile and the cylindrical coordinate system (z, r, θ) and the body-fitted orthogonal coordinate system (t, b, n) obtained by the graphical method, the cylindrical coordinate values ​​of each point on the hub line and wheel arch line in the zr plane are obtained. Then, the cylindrical coordinate values ​​of the center streamline are calculated, where the cylindrical coordinate values ​​of each point on the center streamline are the sum of the corresponding cylindrical coordinate values ​​of each point on the hub line and wheel arch line and divided by 2.

[0035] In one embodiment of the present invention, step S3 includes the following steps:

[0036] Using the cylindrical coordinates of the central streamline as input to the central streamline method, we obtain the axial increment dz and radial increment dr between control points on each segment of the central streamline. Defining the length sL of the central streamline, the length increment between control points on the central streamline is then:

[0037] The length of the center streamline at the inlet of the working wheel is sL1, and the length of the center streamline at the outlet of the working wheel is sL2. The length of the center streamline is calculated from the outlet of the working wheel, i.e., sL2 = 0, while sL1 is sL2 plus the length increment dsL between the control points on each segment of the center streamline.

[0038] In one embodiment of the present invention, step S3 further includes the step:

[0039] Derivation of characteristic function:

[0040] Assume the relative velocity airflow angle β satisfies the following relationship:

[0041]

[0042] In equation (11), K is the exponential value controlling the change of the relative velocity airflow angle within the flow channel, C represents the difference between the cosecant values ​​of the relative velocity airflow angles at the inlet and outlet, and β1 represents the relative velocity airflow angle at the leading edge of the impeller inlet. L =s L2 When = 0, β = β 2，mean ,Right now:

[0043] C=cscβ 2,mean -cscβ1 (12)

[0044] Therefore, we can obtain:

[0045]

[0046] Where β 2，mean The relative velocity airflow angle representing the trailing edge of the streamline at the center of the impeller outlet;

[0047] Define the characteristic function:

[0048]

[0049] From the geometric relationship between the cylindrical coordinate system (z, r, θ) and the body-fitted orthogonal coordinate system (t, b, n), we can obtain:

[0050] Substituting the characteristic function, we get:

[0051]

[0052] In one embodiment of the present invention, in step S3, the value of K ranges from 1 to 20.

[0053] In one embodiment of the present invention, in step S4, the θ coordinate of the central meridian streamline is: θmean'=θmean+dθ; then the θ coordinates of the wheel arch line and the wheel hub line are: θshroud=θhub=θmean'.

[0054] In one embodiment of the present invention, the design method of the working wheel of the cryogenic turbine expander further includes the step: S5, obtaining the three-dimensional shape design of the working wheel by rotating the array using CATIA three-dimensional drawing software.

[0055] This invention obtains the meridional profile of the working wheel through a graphical method, thereby obtaining the (z, r) cylindrical coordinates of each point on the hub line and wheel cover line. Then, the (z, r) cylindrical coordinates of the central streamline are calculated. These are used as input conditions for the central streamline method to obtain the length and characteristic function value of the central meridional streamline. The θ coordinates of the central meridional streamline are calculated in reverse, yielding the θ coordinates of the hub line and wheel cover line, thus obtaining the central flow surface of the working wheel blades. Finally, the three-dimensional shape design of the working wheel is obtained through a rotational array. This invention combines the graphical method with the central streamline method, improving upon previous design methods by addressing the issue of uneven and discontinuous blade flow channel surfaces in the transition area between the parabolic working wheel guide section and the straight blade section, thus improving the operating efficiency of the turbine expander. It also improves the problem of diameter expansion at the blade trailing edge in the central streamline method, facilitating the actual installation of the working wheel.

[0056] The further objects and advantages of the invention will become fully apparent from the following description and accompanying drawings. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the design method of the working wheel of the cryogenic turbine expander according to the present invention.

[0058] Figure 2A and Figure 2B This is a schematic diagram of the meridional profile forming principle using a graphical method in the design method of the working wheel of the low-temperature turbine expander of the present invention.

[0059] Figure 3 This is a schematic diagram of the meridional profile obtained by drawing a diagram in the design method of the working wheel of the low-temperature turbine expander of the present invention.

[0060] Figure 4 This is a geometric diagram showing the relationship between the meridional coordinate system, cylindrical coordinate system, and body-fitted orthogonal coordinate system in the design method of the working wheel of the cryogenic turbine expander of the present invention. Detailed Implementation

[0061] The following description is intended to disclose the present invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art. The basic principles of the invention defined in the following description can be applied to other embodiments, modifications, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the invention.

[0062] Those skilled in the art should understand that, in the disclosure of this invention, the terms "vertical," "horizontal," "up," "down," "front," "back," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0063] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0064] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection, an electrical connection, or a connection that allows for communication; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0065] As a key component of large-scale cryogenic refrigeration systems, the efficiency of the turbine expander significantly impacts the overall performance of the machine. The design of the impeller is a crucial aspect of the turbine expander design process, directly affecting its operating efficiency. Previous design methods suffer from the problem of uneven and discontinuous blade flow surface in the transition region between the impeller guide section and the straight blade section. Therefore, this invention provides a design method for the impeller of a cryogenic turbine expander, optimizing the impeller and enabling efficient programming design.

[0066] The design of impellers for turbo expanders involves more than just finding the optimal blade profile for maximum efficiency; the feasibility of impeller machining must also be considered. While Hasselgruber's center streamline method, which considers the relative flow characteristics of the fluid within the impeller, is comprehensive among various design methods, its meridional profile is "trumpet-shaped," and the expansion of the diameter at the blade trailing edge makes it unsuitable for complete assembly when applied to turbo expander impeller design. Therefore, improvements are necessary. This invention borrows from the center streamline method, considers the relative flow characteristics of the fluid within the impeller, and combines it with a graphical method to address the diameter expansion issue at the blade trailing edge. It designs a method suitable for cryogenic turbo expander impellers, improving upon previous methods by addressing the issue of uneven and discontinuous blade flow channels in the transition area between the parabolic impeller guide section and the straight blade section, and facilitating the actual installation of the impeller.

[0067] Specifically, such as Figure 1 As shown, the design method of the cryogenic turbine expander impeller according to a preferred embodiment of the present invention includes the following steps:

[0068] S1. Obtain the meridional profile of the working wheel of the low-temperature turbine expander by drawing a graph. Based on the coordinates of the control points of the meridional profile, obtain the cylindrical coordinate values ​​of each point on the hub line and the wheel cover line respectively.

[0069] S2. Calculate the cylindrical coordinate value of the center streamline based on the cylindrical coordinate values ​​of each point on the hub line and wheel arch line;

[0070] S3. Using the cylindrical coordinates of the central streamline as the input condition for the central streamline method, the length of the central meridional streamline and the value of the characteristic function are calculated using the central streamline method.

[0071] S4. Based on the length of the central meridian streamline and the value of the characteristic function, the θ coordinate of the central meridian streamline is calculated, and the θ coordinates of the hub line and the wheel cover line are obtained, thus obtaining the central flow surface of the working wheel blade;

[0072] S5. The three-dimensional shape design of the working wheel is obtained by rotating the array using three-dimensional modeling software.

[0073] The following will combine Figures 2A to 4 The specific process of designing the working wheel of a cryogenic turbine expander by combining the drawing method and the center streamline method is described.

[0074] I. Graphical Method

[0075] like Figure 2A As shown, the axial length of the working wheel is taken.

[0076] B z =(0.3-0.4)D1 (1)

[0077] For the hub profile:

[0078] B z1 =B z (2)

[0079]

[0080] For the shroud profile:

[0081] B z2 =B z -L1 (4)

[0082]

[0083] In the above formula, B z1 B z2 These are the axial lengths of the meridional hub profile and the meridional wheel arch profile, respectively, L. r1 L r2 These are the radial lengths of the meridional hub profile and the meridional shroud profile, respectively. D1 is the diameter of the leading edge of the impeller inlet, D'2 is the diameter of the trailing edge of the impeller outlet shroud, D”2 is the diameter of the trailing edge of the impeller outlet hub, and L1 is the height of the blade at the leading edge of the impeller inlet.

[0084] It is understandable that Bz in equation (1) is (0.3-0.4)D1, which comprehensively considers the flow expansion process and flow friction loss of the fluid in the working wheel. It is necessary to meet the expansion pressure and temperature required by the design while minimizing the friction loss during the flow process.

[0085] Taking the meridional hub profile as an example, the axial length B of the meridional hub profile... z1 Its radial length L r1 If the difference is divided into M equal parts, then the length of each part is:

[0086]

[0087] Based on M equal parts, with axial length B respectively z1 With radial length L r1 The intersection points O0, O1, ..., O M Centered on a circle with a radial length L r1 Draw a circle with radius B, and obtain the arc and axial length B respectively. z1 Intersects at points 0, 1, ..., N, where N = M, then the axial length B z1 With radial length L r1 The included angle is also divided into M equal parts, and the angle bisector intersects the corresponding arcs at points P0, P1, ..., P2. N This is the control point of the meridional hub profile.

[0088] It is worth mentioning that in this invention, the subscript 1 of each parameter represents the leading edge of the inlet of the working wheel, the subscript '2 represents the trailing edge of the wheel cover at the outlet of the working wheel, and the subscript "2" represents the trailing edge of the hub at the outlet of the working wheel.

[0089] In addition, it is worth mentioning that the larger the value of M, the more discrete points there are on the profile, and the smoother the meridional profile will be. However, if the value is too large, the amount of calculation will increase and the calculation efficiency will be affected. Therefore, the preferred value range of M is 30 to 50.

[0090] Specifically, such as Figure 2B As shown in this specific embodiment, for the sake of a simpler and clearer illustration, M is set to 5. That is, in this specific embodiment, the axial length B of the meridional hub profile is... z1 Its radial length L r1 The difference is divided into 5 equal parts, and the principle of profile forming is as follows: Figure 2B As shown.

[0091] With the intersection point O0 of the longer side Bz' and the shorter side Lr as the center, and the shorter side length L... r1 Draw a circle with radius B, and the arc intersects the longer side B. z1 They intersect at point 0; the distance between point O1 and point O0 is a. A circle is formed with point O1 as its center and L as its axis. r1 Draw a circle with radius B, and the arc intersects the longer side B. z1 The two circles intersect at point 1; and so on, with O2, O3, O4, and O5 as centers respectively, each intersecting at point L. r1 Draw a circle with radius B, intersecting the longer side B with the circle with radius B. z1 Intersects at points 2, 3, 4, and 5. Then, the longer side Bz1 intersects with the shorter side L. r1 The included angle is also divided into M equal parts. The angle bisector intersects the corresponding arc at points P0, P1, P2, P3, P4, and P5. These five points are the control points of the desired profile. The larger M is, the smoother the profile will be.

[0092] Depend on Figure 2A and Figure 2B The coordinate expression of the control points PN (N = 0, 1, ..., M) of the meridian can be obtained as PN(z N r N ),in,

[0093] z N =B z -(MN)aL r cos(δ N +θ N (7)

[0094]

[0095] In the above formula, z NIt is the axial cylindrical coordinate value of the control point, r N It is the radial cylindrical coordinate value of the control point, δ N It is the longer side B z1 With the short side L r1 The angle value θ after dividing the included angle M into equal parts N It is the center and control point P N The angle between the line connecting the two points and the axial direction.

[0096] It is understandable that the (z, r) cylindrical coordinates of each point on the hub line and wheel arch line are the control point coordinates PN(z) of the meridian profile. N r N ).

[0097] Combining the Law of Cosines, equations (7) and (8) are transformed into:

[0098]

[0099]

[0100] The calculation methods for the cylindrical coordinate values ​​of the meridional wheel arch profile and the meridional wheel hub profile are the same. The cylindrical coordinate values ​​of the meridional wheel arch profile are calculated using the same process as for the cylindrical coordinate values ​​of the meridional wheel hub profile. The obtained wheel hub profile and wheel arch profile are as follows: Figure 3 As shown, this profile is the meridional profile of the turbine expander impeller.

[0101] In other words, the hub profile and wheel cover profile obtained from the control point coordinates of the meridional wheel cover profile and the meridional wheel hub profile are the meridional profiles for designing the turbine expander impeller.

[0102] II. Center Streamline Method

[0103] like Figure 4 As shown in the figure, the two coordinate systems are a cylindrical coordinate system (z, r, θ) and a body-fitted orthogonal coordinate system (t, b, n). Here, coordinate z represents the axial direction of the cylindrical coordinate system, r represents the radial direction, and θ represents the circumferential direction. Coordinate t represents the streamline direction at the center of the flow channel, coordinate b represents the width direction between the pressure and suction surfaces of the flow channel, coordinate n represents the depth direction of the flow channel, β is the relative velocity airflow angle, ω is the angular velocity of the impeller, and δ is the angle between the meridional coordinate direction and the axial coordinate direction. Simultaneously, a meridional coordinate s is defined to connect the cylindrical coordinate system and the body-fitted orthogonal coordinate system; coordinate s lies in the zr plane of the cylindrical coordinate system.

[0104] It is understandable that, such as Figure 4 Based on the geometric relationship, after obtaining the coordinates of the meridional plane profile using the graphical method, the length of the central streamline of the meridional plane can be obtained. The length of the central streamline is calculated from the outlet of the impeller, that is, the length of the central streamline at the outlet of the impeller is 0.

[0105] Specifically, such as Figure 4 Based on the geometric relationships, after obtaining the meridional profile using a graphical method, the cylindrical coordinates of each point on the hub line and wheel arch line within the zr plane can be obtained. Then, the cylindrical coordinates of the central streamline are calculated; that is, the cylindrical coordinates of each point on the central streamline are the sum of the corresponding cylindrical coordinates of the hub line and wheel arch line points, divided by 2. This yields the axial increment dz and radial increment dr between each control point on the central streamline.

[0106] Define the length sL of the center streamline as follows: the length increment between control points on the center streamline. The length of the center streamline at the inlet of the impeller is sL1, and the length of the center streamline at the outlet of the impeller is sL2. The length of the center streamline is measured from the outlet of the impeller, i.e., sL2 = 0, while sL1 is sL2 plus the length increment dsL between the control points on each segment of the center streamline.

[0107] Derivation of characteristic function:

[0108] Assume the relative velocity airflow angle β satisfies the following relationship:

[0109]

[0110] In equation (11), K is the exponential value controlling the change of the relative velocity airflow angle within the flow channel, generally between 1 and 20; C represents the difference between the cosecant values ​​of the relative velocity airflow angles at the inlet and outlet, β1 represents the relative velocity airflow angle at the leading edge of the impeller inlet, and the value of C is determined by known conditions. L =s L2 When = 0, β = β 2，mean ,Right now:

[0111] C=cscβ 2,mean -cscβ1 (12)

[0112] Therefore, we can obtain:

[0113]

[0114] Where β 2，mean The relative velocity airflow angle representing the trailing edge of the streamline at the center of the impeller outlet;

[0115] Define the characteristic function:

[0116]

[0117] This characteristic function characterizes the variation of the relative velocity airflow angle within the working impeller channel.

[0118] Depend on Figure 4The geometric relationship between the cylindrical coordinate system (z, r, θ) and the body-fitted orthogonal coordinate system (t, b, n) can be obtained as follows: Substituting the characteristic function, we get:

[0119]

[0120] It is understandable that formulas (14)-(15) are the calculation process of the θ coordinates of the hub line and the wheel arch line. The θ coordinate of the center meridian streamline is the same as the θ coordinates of the hub line and the wheel arch line.

[0121] It is also understandable that this invention derives the mathematical expression of the characteristic function of the central streamline method by assuming that the relative velocity airflow angle satisfies a certain variation relationship. Moreover, this invention uses the (z, r) cylindrical coordinates of the meridional profile obtained by the graphical method as input conditions to calculate the length of the central meridional streamline and the value of the characteristic function, and then calculates the θ coordinate of the central meridional streamline in reverse.

[0122] Specifically, the present invention calculates the θ coordinate of the central meridian streamline as follows based on reverse calculation: θmean'=θmean+dθ; then the θ coordinates of the wheel arch line and the wheel hub line are: θshroud=θhub=θmean'. In other words, the θ coordinates of the wheel arch, wheel hub, and central meridian streamline are the same.

[0123] It is worth mentioning that the projection of the central flow surface onto the zr plane is the meridional surface of the working wheel. Based on the θ coordinate of the central meridional streamline, the central flow surface of the working wheel blade can be obtained. Finally, the three-dimensional shape design of the working wheel is obtained through a rotation array.

[0124] Understandably, this invention obtains the meridional profile of the working wheel through a graphical method, thereby obtaining the (z, r) cylindrical coordinates of each point on the hub line and wheel arch line. Then, the (z, r) cylindrical coordinates of the central streamline are calculated. These are used as input conditions for the central streamline method to obtain the length of the central meridional streamline and the value of its characteristic function. The θ coordinates of the central meridional streamline are calculated in reverse, thereby obtaining the θ coordinates of the hub line and wheel arch line, and thus obtaining the central flow surface of the working wheel blade. Finally, the three-dimensional model design of the working wheel is obtained by rotating the array using CATIA three-dimensional drawing software.

[0125] It is worth mentioning that the present invention can use CATIA 3D modeling software to rotate and array to obtain the 3D shape design of the working wheel, or it can use other 3D modeling software with rotation and array functions to obtain the 3D model of the working wheel. The present invention does not limit this.

[0126] It is also understandable that this invention combines the drawing method with the center streamline method, which not only improves the problem of the non-smooth and continuous blade flow channel surface in the transition area between the parabolic working wheel guide section and the straight blade section in the previous design method, thus improving the operating efficiency of the turbine expander; it also improves the problem of the diameter expansion at the trailing edge of the blade in the center streamline method, which facilitates the actual installation of the working wheel.

[0127] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0128] The above embodiments merely illustrate preferred implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention should be determined by the appended claims.

Claims

1. A design method for a working impeller of a low-temperature turbine expander, characterized in that: Including the following steps: S1. Obtain the meridional profile of the working wheel of the low-temperature turbine expander by drawing a graph. Based on the coordinates of the control points of the meridional profile, obtain the cylindrical coordinate values ​​of each point on the hub line and the wheel cover line respectively. S2. Calculate the cylindrical coordinate value of the center streamline based on the cylindrical coordinate values ​​of each point on the hub line and wheel arch line; S3. Using the cylindrical coordinates of the central streamline as the input condition for the central streamline method, the length of the central meridional streamline and the value of the characteristic function are calculated using the central streamline method. S4. Based on the length of the central meridian streamline and the value of the characteristic function, the central meridian streamline is calculated. θ By using the coordinates, you can obtain the hub line and the wheel arch line. θ The coordinates are used to obtain the flow surface at the center of the impeller blades; Step S1 includes the following steps: Take the axial length of the working wheel （1） For the hub profile: （2） （3） For the shroud profile: （4） （5） In the above formula, B z1 , B z2 These are the axial lengths of the meridional hub profile and the meridional wheel arch profile, respectively. L r1 , L r2 These are the radial lengths of the meridional hub profile and the meridional wheel arch profile, respectively. D 1 is the diameter of the leading edge of the impeller inlet. D’ 2 is the diameter of the trailing edge of the outlet wheel cover of the working wheel. D’’ 2 is the diameter of the trailing edge of the wheel hub at the outlet of the working wheel. L 1 is the height of the leading edge blades at the inlet of the impeller; Taking the meridional hub profile as an example, the axial length of the meridional hub profile... B z1 Its radial length L r1 The difference is divided into M If divided into equal parts, the length of each part is: （6） based on M Divide into equal parts, each by axial length B z1 With radial length L r1 The intersection points O0, O1, ..., O M Centered on the circle, with radial length L r1 Draw a circle with radius , and obtain the arc and axial length respectively. B z1 Intersects at points 0, 1, ..., N, where N = M, then the axial length is... B z1 With radial length L r1 The included angle is also divided into M Divide the circle into equal parts, and the points where the angle bisector intersects the corresponding arc. P 0、 P 1, ... P N These are the control points for the hub profile of the meridional plane; Therefore, the control point P of the meridional hub profile is obtained. N The coordinate expression for (N=0, 1, ..., M) is P(z N r N ),in, （7） （8） In the above formula, z N These are the axial cylindrical coordinate values ​​of the control points. r N These are the radial cylindrical coordinates of the control points. δ N It is the longer side B z1 With the shorter side L r1 included angle M The angle values ​​after equal division θ N The center and control points P N The angle between the line connecting the two points and the axial direction; Combining the Law of Cosines, equations (7) and (8) are transformed into: （9） （10） The calculation methods for the cylindrical coordinate values ​​of the meridional wheel cover profile and the meridional wheel hub profile are the same. The wheel hub profile and wheel cover profile obtained from the control point coordinates of the meridional wheel cover profile and the meridional wheel hub profile are the meridional profiles for designing the turbine expander working wheel. Step S2 includes the following steps: Based on meridian coordinates Establish a cylindrical coordinate system ( , , ) and the body-fitted orthogonal coordinate system ( , , Geometric relationship of ): where coordinates z Let be the axis of the cylindrical coordinate system. r For the radial direction in cylindrical coordinates, θ The circumferential direction in a cylindrical coordinate system; coordinates The direction of the streamline at the center of the flow channel, coordinates The width direction between the pressure surface and suction surface of the flow channel, coordinates The direction of flow channel depth is represented by the meridional coordinates. In cylindrical coordinate system ( , , )of - In the plane; Based on the meridian profile and cylindrical coordinate system obtained by the graphical method , , ) and the body-fitted orthogonal coordinate system ( , , The geometric relationship of ) is obtained - The cylindrical coordinates of each point on the hub line and wheel arch line in the plane are calculated, and then the cylindrical coordinates of the center streamline are calculated. The cylindrical coordinates of each point on the center streamline are the sum of the corresponding cylindrical coordinates of each point on the hub line and wheel arch line and divided by 2. Step S3 includes the following steps: Using the cylindrical coordinates of the central streamline as input to the central streamline method, the axial increments between control points along each segment of the central streamline are obtained. dz and radial increment dr Define the length of the center streamline. sL The length increment between control points on the central streamline is: ; The streamline length of the inlet center of the working wheel is: sL1 The streamline length of the outlet center of the working wheel is sL2 The length of the center streamline is measured from the outlet of the workpiece, that is... sL2 =0, and sL1 yes sL2 Add the length increments between control points on each segment's center streamline. dsL .

2. The design method for the working wheel of a cryogenic turbine expander according to claim 1, characterized in that, In step S1, the value of M ranges from 30 to 50.

3. The design method for the working impeller of a low-temperature turbine expander according to claim 2, characterized in that, Step S3 further includes the following steps: Derivation of characteristic function: Assuming relative velocity airflow angle The following relationship must be satisfied: （11） In equation (11), The C value represents the difference between the cosecant values ​​of the relative velocity airflow angle at the inlet and outlet, used to control the exponential variation of the relative velocity airflow angle within the flow channel. β 1 represents the relative velocity airflow angle at the leading edge of the impeller inlet, when hour, ,Right now: （12） Therefore, we can obtain: （13） in β 2，mean The relative velocity airflow angle representing the trailing edge of the streamline at the center of the impeller outlet; definition Characteristic function: （14） From cylindrical coordinate system ( , , ) and the body-fitted orthogonal coordinate system ( , , From the geometric relationship, we can obtain: Substituting the characteristic function into the equation yields: （15）。 4. The design method for the working impeller of a cryogenic turbine expander according to claim 3, characterized in that, In step S3, The value range is 1 to 20.

5. The design method for the working wheel of a cryogenic turbine expander according to claim 3, characterized in that, In step S4, the central meridian streamline θ The coordinates are: θmean' = θmean + dθ The wheel arch line and the wheel hub line θ The coordinates are: θshroud = θhub = θmean' .

6. The design method for the working impeller of a cryogenic turbine expander according to any one of claims 1 to 5, characterized in that, It also includes step S5: obtaining the three-dimensional shape design of the working wheel by rotating the array using CATIA three-dimensional modeling software.

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