CN117332546A - Design method of working wheel of low-temperature turbine expander - Google Patents

Design method of working wheel of low-temperature turbine expander Download PDF

Info

Publication number
CN117332546A
CN117332546A CN202210723531.8A CN202210723531A CN117332546A CN 117332546 A CN117332546 A CN 117332546A CN 202210723531 A CN202210723531 A CN 202210723531A CN 117332546 A CN117332546 A CN 117332546A
Authority
CN
China
Prior art keywords
line
meridian
wheel
central
hub
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210723531.8A
Other languages
Chinese (zh)
Inventor
柯长磊
彭楠
李空荣
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Technical Institute of Physics and Chemistry of CAS
Original Assignee
Technical Institute of Physics and Chemistry of CAS
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Technical Institute of Physics and Chemistry of CAS filed Critical Technical Institute of Physics and Chemistry of CAS
Priority to CN202210723531.8A priority Critical patent/CN117332546A/en
Publication of CN117332546A publication Critical patent/CN117332546A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/18—Manufacturability analysis or optimisation for manufacturability
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/20—Design reuse, reusability analysis or reusability optimisation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Turbine Rotor Nozzle Sealing (AREA)

Abstract

The invention relates to a design method of a working wheel of a low-temperature turbine expander, which comprises the following steps: obtaining a meridian plane molded line of the running wheel by a mapping method, namely obtaining (z, r) column coordinate values of each point on the hub line and the wheel cover line, and then calculating (z, r) column coordinate values of the central streamline; taking the central meridian length as an input condition of a central streamline method to obtain the length of a central meridian streamline and the value of a characteristic function; the theta coordinates of the central meridian line are obtained through reverse calculation, namely the theta coordinates of the hub line and the wheel cover line can be obtained, and therefore the central flow surface of the working wheel blade is obtained; finally, the three-dimensional modeling design of the working wheel is obtained through rotating the array; the invention combines the drawing method with the central streamline method, thereby improving the problem that the curved surface of the blade runner in the transition area of the flow guiding section and the straight blade section of the paraboloid formed working wheel in the traditional design method is not smooth and continuous, and improving the operation efficiency of the turbine expander; the problem of diameter expansion at the tail edge of the vane by the central streamline method is improved, and the actual installation of the running wheel is facilitated.

Description

Design method of working wheel of low-temperature turbine expander
Technical Field
The invention relates to the technical field of low-temperature turboexpanders, in particular to a design method of a working wheel of a low-temperature turboexpander.
Background
The low temperature turboexpander is used as a main cold producing component, and is one of core components in most low temperature refrigeration systems. The stability and the operation efficiency of the system greatly influence the energy consumption and the efficiency of the whole system. Due to its wide application, more and more researchers have been put into the related research in recent years. Several monographs also discuss in detail the basic concepts and design methods of turboexpanders. Because the temperature of the inlet medium is low, the expansion ratio is large, and especially at a small flow rate, the diameter of the running wheel is smaller, the specific enthalpy of the expander is reduced greatly, and the rotating speed of the rotor of the expander is higher in order to achieve higher heat insulation efficiency. Therefore, the small size and high rotating speed are obvious characteristics of the low-temperature turbine expander. At present, the theory and the design method of the low-temperature turbine expander do not have a general rule, and the conventional design method has the problem that the curved surface of the blade runner in the transition area of the guide section and the straight blade section of the working wheel is not smooth and continuous.
Based on the concept of Wu Zhonghua of ternary flow of turbomachinery, hasselgrouber proposes a calculation method for designing a working wheel blade profile of a rotating machine, the method obtains a cylindrical coordinate parameter of a central streamline from an inlet front edge to an outlet tail edge of a working wheel through a characteristic function, obtains a meridian plane line of the working wheel through a geometric relationship between the central streamline and a hub line as well as a wheel cover line, and finally completes blade modeling according to an angle value of the cylindrical coordinate parameter and the meridian plane line. However, the meridian profile obtained by the method is of a horn shape, and the expansion of the diameter at the tail edge of the blade makes the method incapable of mounting the whole machine when the method is applied to the modeling of the turbine expander working wheel.
Disclosure of Invention
The invention aims to provide a design method of a working wheel of a low-temperature turbine expander, which not only solves the problem that the curved surface of a blade flow channel in the transition area of a parabolic flow guiding section and a straight blade section of the working wheel is not smooth and continuous in the conventional design method, but also facilitates the actual installation of the working wheel and provides a thinking for the design of the working wheel of the turbine expander in the future.
The invention provides a design method of a working wheel of a low-temperature turbine expander, which comprises the following steps:
s1, obtaining a meridian plane molded line of a working wheel of a low-temperature turbine expander by a mapping method, and respectively obtaining column coordinate values of each point on a hub line and a wheel cover line based on control point coordinates of the meridian plane molded line;
s2, calculating column coordinate values of a central streamline based on column coordinate values of points on the hub line and the wheel cover line;
s3, taking the column coordinate values of the central streamline as input conditions of the central streamline method, and calculating to obtain the length of the central meridian streamline and the value of the characteristic function through the central streamline method;
and S4, calculating to obtain the theta coordinates of the central meridian line based on the length of the central meridian line and the value of the characteristic function, and obtaining the theta coordinates of the hub line and the wheel cover line, thereby obtaining the central flow surface of the working wheel blade.
In an embodiment of the present invention, the step S1 includes the steps of:
taking the axial length of the running wheel
B z ＝(0.3-0.4)D 1 (1)
For HUB (HUB) profile:
B z1 ＝B z (2)
for the wheel cover (SHROUD) profile:
B z2 ＝B z -L 1 (4)
in the above, B z1 、B z2 The axial lengths of the meridian hub molded line and the meridian wheel cover molded line are respectively L r1 、L r2 Respectively meridian hub molded linesAnd radial length of meridian wheel cover molded line D 1 Is the diameter of the front edge of the inlet of the working wheel, D' 2 Is the diameter of the tail edge of the wheel cover of the outlet of the working wheel, D' 2 Is the diameter of the tail edge of the outlet hub of the working wheel, L 1 Is the height of the front edge blade of the inlet of the working wheel;
taking meridian hub molded lines as an example, taking the axial length B of the meridian hub molded lines z1 And its radial length L r1 The difference is M equal parts, each equal part length is:
based on M equal parts, respectively with axial length B z1 And radial length L r1 Intersection point O of (2) 0 、O 1 ……、O M As the center of a circle, with radial length L r1 For making a circle with radius, respectively obtaining an arc and an axial length B z1 Intersecting at points 0,1, … …, N, where n=m, then the axial length B will be z1 And radial length L r1 The included angle of (2) is also divided into M equal parts, and the intersection points P of the angular bisectors and the corresponding circular arcs respectively 0 、P 1 、……、P N The control point of the meridian hub molded line is the control point;
thereby obtaining the control point P of the meridian hub molded line N (n=0, 1, …, M) has a coordinate expression of P (z) N ，r N ) Wherein, the method comprises the steps of, wherein,
z N ＝B z -(M-N)a-L r cos(δ N +θ N ) (7)
in the above, z N Is the axial column coordinate value of the control point, r N Is the radial column coordinate value delta of the control point N Is a long side B z1 And short side L r1 Angle value, θ after equal division of angle M N Is the center of a circle and the control point P N An included angle between the connecting line and the axial direction;
in combination with the cosine law, equations (7) and (8) are transformed into:
the calculation modes of column coordinate values of the meridian wheel cover molded line and the meridian hub molded line are the same, and the hub molded line and the wheel cover molded line obtained by the control point coordinates of the meridian wheel cover molded line and the meridian hub molded line are the meridian molded line for designing the working wheel of the turbine expander.
In an embodiment of the present invention, in the step S1, the value of M ranges from 30 to 50.
In an embodiment of the present invention, the step S2 includes the steps of:
establishing a geometrical relationship between a cylindrical coordinate system (z, r, theta) and a patch orthogonal coordinate system (t, b, n) based on meridian coordinates s: wherein 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 flow line direction of 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 meridian coordinate s is in the z-r plane of a cylindrical coordinate system (z, r, theta);
and obtaining column coordinate values of points on the hub line and the wheel cover line in the z-r plane based on the geometric relationship between the meridian plane and the column coordinate system (z, r, theta) obtained by a mapping method and the body-attached orthogonal coordinate system (t, b, n), and then calculating the column coordinate values of the central streamline, wherein the column coordinate values of the points on the central streamline are obtained by adding the column coordinate values of the points on the corresponding hub line and the wheel cover line and dividing by 2.
In an embodiment of the present invention, the step S3 includes the steps of:
taking the column coordinate value of the central streamline as the input condition of the central streamline method to obtain the axial direction increment dz and the radial direction increment dr between the control points of each section on the central streamline, and definingThe length of the central streamline sL, the length increment between the control points on the central streamline is:
wherein the length of the central streamline of the inlet of the running wheel is sL1, the length of the central streamline of the outlet of the running wheel is sL2, the length of the central streamline is calculated from the outlet of the running wheel, namely sL2=0, and sL1 is the length increment dsL between the control points on the central streamline of each section added by sL2.
In an embodiment of the present invention, the step S3 further includes the steps of:
and (3) derivation of characteristic functions:
the relative velocity air flow angle β is assumed to satisfy the following relationship:
in the formula (11), K is an index value for controlling the change of the relative velocity air flow angle in the flow channel, C is the difference of the residual values of the inlet and outlet relative velocity air flow angles, and beta 1 Air flow angle representing relative velocity of leading edge of inlet of running wheel, when s L ＝s L2 When=0, β=β 2，mean The method comprises the following steps:
C＝cscβ 2,mean -cscβ 1 (12)
the following steps can be obtained:
wherein beta is 2，mean A relative velocity air flow angle representing the leading edge of the rotor outlet center streamline;
defining a characteristic function:
the geometrical relationship between the cylindrical coordinate system (z, r, θ) and the orthographic coordinate system (t, b, n) of the body can be obtained:
bringing the feature function into availability:
in an embodiment of the present invention, in the step S3, the value of K ranges from 1 to 20.
In an embodiment of the present invention, in the step S4, the θ coordinates of the central meridian line are: θmean' =θmean+dθ; the theta coordinates of the wheel cover line and the hub line are: θshroud=θhub=θmean'.
In one embodiment of the present invention, the method for designing a working wheel of a low temperature turboexpander further comprises the steps of: and S5, rotating the array through CATIA three-dimensional drawing software to obtain the three-dimensional modeling design of the running wheel.
The invention obtains the meridian plane molded line of the running wheel by a mapping method, namely, the (z, r) column coordinate values of each point on the hub line and the wheel cover line can be obtained, and then the (z, r) column coordinate values of the central streamline are calculated; taking the central meridian length as an input condition of a central streamline method to obtain the length of a central meridian streamline and the value of a characteristic function; the theta coordinates of the central meridian line are obtained through reverse calculation, namely the theta coordinates of the hub line and the wheel cover line can be obtained, and therefore the central flow surface of the working wheel blade is obtained; finally, the three-dimensional modeling design of the running wheel is obtained through rotating the array. The invention combines the drawing method with the central streamline method, thereby improving the problem that the curved surface of the blade runner in the transition area of the flow guiding section and the straight blade section of the paraboloid formed working wheel in the traditional design method is not smooth and continuous, and improving the operation efficiency of the turbine expander; the problem of diameter expansion at the tail edge of the vane by the central streamline method is improved, and the actual installation of the running wheel is facilitated.
Further objects and advantages of the present invention will become fully apparent from the following description and the accompanying drawings.
Drawings
FIG. 1 is a block flow diagram of a method for designing a low temperature turboexpander impeller in accordance with the present invention.
Fig. 2A and fig. 2B are schematic diagrams of meridian plane profile forming by using a drawing method in the design method of the working wheel of the low-temperature turboexpander.
FIG. 3 is a schematic view of a meridian plane profile obtained by a mapping method in the design method of the working wheel of the low-temperature turboexpander.
Fig. 4 is a geometric relationship diagram of meridian coordinates, a cylindrical coordinate system and a patch orthogonal coordinate system in the design method of the working wheel of the low-temperature turboexpander.
Detailed Description
The following description is presented to enable one of ordinary skill in the art to make and use the invention. The preferred embodiments in the following description are by way of example only and other obvious variations will occur to those skilled in the art. The basic principles of the invention defined in the following description may be applied to other embodiments, variations, modifications, equivalents, and other technical solutions without departing from the spirit and scope of the invention.
It will be appreciated by those skilled in the art that in the present disclosure, the terms "vertical," "transverse," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," etc. refer to an orientation or positional relationship based on that shown in the drawings, which is merely for convenience of description and to simplify the description, and do not indicate or imply that the apparatus or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore the above terms should not be construed as limiting the present invention.
It will be understood that the terms "a" and "an" should be interpreted as referring to "at least one" or "one or more," i.e., in one embodiment, the number of elements may be one, while in another embodiment, the number of elements may be plural, and the term "a" should not be interpreted as limiting the number.
In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically connected, electrically connected or can be communicated with each other; can be directly connected or indirectly connected through an intermediate medium, and can be communicated with the inside of two elements or the interaction relationship of the two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
The efficiency of the turbo expander serving as a key component of a large-scale low-temperature refrigerating system influences the performance of the whole machine to a great extent. The design of the working wheel is an important link in the design process of the turbine expander, and the operation efficiency of the turbine is directly influenced. The traditional design method has the problem that the curved surface of the blade runner in the transition area of the guide section and the straight blade section of the working wheel is not smooth and continuous. Therefore, the invention provides a design method of the working wheel of the low-temperature turboexpander, optimizes the working wheel of the turboexpander and can carry out efficient programming design.
For the design of the turbine expander running wheel, not only the optimal blade profile is found to achieve the maximum running efficiency, but also the feasibility of impeller machining is considered. The central streamline method proposed by Hasselgrouber considers the relative flow characteristics of fluid in the working wheel, so that the method is comprehensive in a plurality of modeling design methods, but meridian surface molded lines are horn-shaped, and the expansion of the diameter at the tail edge of a blade can not be used for installing the whole machine when the method is applied to the modeling of the working wheel of the turbine expander, so that certain improvement is needed for the method. The invention designs a design method suitable for the working wheel of the low-temperature turbine expander by taking reference to a central streamline method, taking the relative flow characteristic of fluid in the working wheel into consideration, and improving the expansion problem of the diameter at the tail edge of a blade by combining with a drawing method, thereby improving the problem that the curved surface of the blade runner in the transition region of a flow guiding section and a straight blade section of the working wheel formed by paraboloids is not smooth and continuous in the traditional design method, and facilitating the practical installation of the working wheel.
Specifically, as shown in fig. 1, the design method of the working wheel of the low-temperature turboexpander according to a preferred embodiment of the present invention comprises the following steps:
s1, obtaining a meridian plane molded line of a working wheel of a low-temperature turbine expander by a mapping method, and respectively obtaining column coordinate values of each point on a hub line and a wheel cover line based on control point coordinates of the meridian plane molded line;
s2, calculating column coordinate values of a central streamline based on column coordinate values of points on the hub line and the wheel cover line;
s3, taking the column coordinate values of the central streamline as input conditions of the central streamline method, and calculating to obtain the length of the central meridian streamline and the value of the characteristic function through the central streamline method;
s4, calculating to obtain the theta coordinates of the central meridian line based on the length of the central meridian line and the value of the characteristic function, namely obtaining the theta coordinates of the hub line and the wheel cover line, and obtaining the central flow surface of the working wheel blade;
s5, rotating the array through three-dimensional drawing software to obtain the three-dimensional modeling design of the running wheel.
The specific process of designing a low temperature turboexpander rotor in combination with the mapping method and the center flow method will be described below with reference to fig. 2A to 4.
1. Mapping method
As shown in fig. 2A, the axial length of the running wheel is taken
B z ＝(0.3-0.4)D 1 (1)
For HUB (HUB) profile:
B z1 ＝B z (2)
for the wheel cover (SHROUD) profile:
B z2 ＝B z -L 1 (4)
in the above, B z1 、B z2 The axial lengths of the meridian hub molded line and the meridian wheel cover molded line are respectively L r1 、L r2 Radial lengths of meridian hub molded line and meridian wheel casing molded line respectively, D 1 Is the diameter of the front edge of the inlet of the working wheel, D' 2 Is the diameter of the tail edge of the wheel cover of the outlet of the working wheel, D' 2 Is the diameter of the tail edge of the outlet hub of the working wheel, L 1 Is the front edge blade height of the inlet of the working wheel.
It will be appreciated that Bz in formula (1) is (0.3-0.4) D 1 The flow expansion process and the flow friction loss of the fluid in the working wheel are comprehensively considered, so that the expansion pressure and the expansion temperature required by design are achieved, and the friction loss in the flow process is reduced as much as possible.
Taking meridian hub molded lines as an example, taking the axial length B of the meridian hub molded lines z1 And its radial length L r1 The difference is M equal parts, each equal part length is:
based on M equal parts, respectively with axial length B z1 And radial length L r1 Intersection point O of (2) 0 、O 1 ……、O M As the center of a circle, with radial length L r1 For making a circle with radius, respectively obtaining an arc and an axial length B z1 Intersecting at points 0,1, … …, N, where n=m, then the axial length B will be z1 And radial length L r1 The included angle of (2) is also divided into M equal parts, and the intersection points P of the angular bisectors and the corresponding circular arcs respectively 0 、P 1 、……、P N Then it is the control point of meridian hub profile.
It should be noted that, in the present invention, the corner mark 1 of each parameter represents the leading edge of the inlet of the running wheel, the corner mark' 2 represents the trailing edge of the outlet wheel cover of the running wheel, and the corner mark "2" represents the trailing edge of the outlet wheel hub of the running wheel.
In addition, it is also worth mentioning that the larger the value of M, the more discrete points on the contour line, the smoother the obtained meridian line, but the larger the numerical value is, the more the calculation efficiency is affected, so the value range of M is preferably 30-50.
Specifically, as shown in fig. 2B, in this embodiment, for more concise and clear drawing, the value of M is 5, that is, in this embodiment, the axial length B of the meridian hub profile will be z1 And its radial length L r1 The difference is 5 equal parts, and the molding principle of the molded line is shown in fig. 2B.
With the intersection point O of the long side Bz' and the short side Lr 0 As the center of a circle, with the length L of the shorter side r1 For making a circle with a radius, an arc and a long side B z1 Intersection at point 0; point O 1 And point O 0 A distance of a, at a point O 1 As the center of a circle, also take L r1 For making a circle with a radius, an arc and a long side B z1 Intersection at point 1; analogize in the same way, respectively by O 2 、O 3 、O 4 、O 5 All take L as the center of a circle r1 Is round with radius and is respectively connected with the long side B z1 Intersecting at 2, 3, 4, 5. Then the long side Bz1 and the short side L r1 The included angle is also divided into M equal parts, and the angular bisectors respectively intersect with the corresponding circular arcs at a point P 0 、P 1 、P 2 、P 3 、P 4 、P 5 These five points are the control points of the profile, and the larger M the smoother the resulting profile.
From fig. 2A and 2B, the coordinate expression of the control point PN (n=0, 1, …, M) of the meridian line is PN (z) N ，r N ) Wherein, the method comprises the steps of, wherein,
z N ＝B z -(M-N)a-L r cos(δ N +θ N ) (7)
in the above, z N Is the axial column coordinate value of the control point, r N Is the radial column coordinate value delta of the control point N Is a long side B z1 And short side L r1 Angle value, θ after equal division of angle M N Is the center of a circle and the control point P N An included angle between the connecting line and the axial direction.
It can be understood that the (z, r) column coordinate values of each point on the hub line and the wheel cover line are the control point coordinate PN (z) of the meridian line N ，r N )。
In combination with the cosine law, equations (7) and (8) are transformed into:
the calculation modes of the column coordinate values of the meridian wheel cover molded line and the meridian wheel hub molded line are the same, the column coordinate values of the meridian wheel cover molded line are calculated according to the same calculation process with the column coordinate values of the meridian wheel hub molded line, the respectively obtained wheel hub molded line and the wheel cover molded line are shown in figure 3, and the molded line is the meridian molded line for designing the working wheel of the turbine expander.
That is, the hub profile and the shroud profile obtained from the control point coordinates of the meridional shroud profile and the meridional hub profile are meridional profiles for designing the turbine expander running wheel.
2. Central streamline method
As shown in fig. 4, the two coordinate systems in the figure are respectively a cylindrical coordinate system (z, r, θ) and a patch orthogonal coordinate system (t, b, n). Wherein 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 flow line direction of 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, the coordinate n is the depth direction of the flow channel, the beta is the air flow angle with relative speed, the omega is the angular speed of the running wheel, and the delta is the included angle between the meridian coordinate direction and the axial coordinate direction. Meanwhile, meridian coordinates s are defined to relate the cylindrical coordinate system to the patch orthogonal coordinate system, and the coordinates s are in the z-r plane of the cylindrical coordinate system.
It will be appreciated that, as in the geometric relationship of fig. 4, after the meridian plane line coordinates are obtained by the mapping method, the length of the meridian plane central streamline is obtained, wherein the central streamline length is calculated from the running wheel outlet, i.e. the running wheel outlet central streamline length is 0.
Specifically, as shown in the geometric relationship of fig. 4, after the meridian plane line is obtained by a mapping method, the column coordinate values of each point on the hub line and the wheel cover line in the z-r plane can be obtained, and then the column coordinate value of the central streamline is calculated, namely, the column coordinate values of each point on the central streamline are the column coordinate values of each point on the corresponding hub line and wheel cover line, and are added and divided by 2. Thereby obtaining the axial direction increment dz and the radial direction increment dr between the control points of each section on the central flow line.
Defining the length sL of the central streamline, the length increment between control points on the central streamlineThe impeller inlet central streamline length sL1 and the impeller outlet central streamline length sL2. The length of the centerline is calculated from the wheel exit, i.e., sl2=0, while sL1 is the sum of sL2 plus the length increment dsL between the control points on each segment centerline.
And (3) derivation of characteristic functions:
the relative velocity air flow angle β is assumed to satisfy the following relationship:
in the formula (11), K is an index value for controlling the change of the relative velocity air flow angle in the flow channel, and is generally between 1 and 20; the value C represents the difference between the residual values of the air flow angles of the inlet and outlet relative speeds, beta 1 The air flow angle representing the relative velocity of the leading edge of the inlet of the rotor, the value C being determined by known conditions, when s L ＝s L2 When=0, β=β 2，mean The method comprises the following steps:
C＝cscβ 2,mean -cscβ 1 (12)
the following steps can be obtained:
wherein beta is 2，mean A relative velocity air flow angle representing the leading edge of the rotor outlet center streamline;
defining a characteristic function:
the characteristic function characterizes the change in relative velocity air flow angle within the rotor flow channel.
The geometrical relationship between the cylindrical coordinate system (z, r, θ) and the orthographic coordinate system (t, b, n) of the patch in fig. 4 can be obtained:bringing the feature function into availability:
it will be appreciated that equations (14) - (15) are a calculation of the theta coordinates of the hub line and the shroud line. The θ coordinates of the central meridian line are the same as those of the hub line and the shroud line.
It will also be appreciated that the present invention derives a mathematical representation of the characteristic function of the central streamline by assuming that the relative velocity air flow angle satisfies a certain relationship of variation. The invention also uses the meridian plane (z, r) cylindrical coordinates obtained by the mapping method as input conditions to calculate the length of the central meridian line and the value of the characteristic function, and reversely calculates the theta coordinates of the central meridian line.
Specifically, the θ coordinates of the central meridian line obtained by the method according to the reverse calculation are as follows: θmean' =θmean+dθ; the theta coordinates of the wheel cover line and the hub line are: θshroud=θhub=θmean'. That is, the θ coordinates of the wheel cover, the hub, and the central meridian line are the same.
It is worth mentioning that the projection of the central flow surface in the z-r plane is the meridian surface of the running wheel, the central flow surface of the blade of the running wheel can be obtained based on the theta coordinates of the central meridian line, and finally the three-dimensional modeling design of the running wheel is obtained through the rotary array.
It can be understood that the invention obtains the meridian plane line of the running wheel by a drawing method, namely, the (z, r) column coordinate values of each point on the hub line and the wheel cover line can be obtained, and then the (z, r) column coordinate values of the central streamline are calculated; taking the central meridian length as an input condition of a central streamline method to obtain the length of a central meridian streamline and the value of a characteristic function; the theta coordinates of the central meridian line are obtained through reverse calculation, namely the theta coordinates of the hub line and the wheel cover line can be obtained, and therefore the central flow surface of the working wheel blade is obtained; and finally, rotating the array through CATIA three-dimensional drawing software to obtain the three-dimensional modeling design of the running wheel.
It is worth mentioning that the invention can adopt CATIA three-dimensional drawing software to rotate the array to obtain the three-dimensional modeling design of the running wheel, can also adopt other three-dimensional drawing software with function of rotating the array to obtain the three-dimensional model of the running wheel, the invention is not limited to this.
It can be further understood that the invention combines the drawing method with the central streamline method, thereby improving the problem of unsmooth and continuous curved surfaces of the blade flow passages in the transition area of the parabolic formed impeller flow guide section and the straight blade section in the traditional design method and improving the operation efficiency of the turbine expander; the problem of diameter expansion at the tail edge of the vane by the central streamline method is improved, and the actual installation of the running wheel is facilitated.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The foregoing examples only represent preferred embodiments of the present invention, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.

Claims (9)

1. A design method of a working wheel of a low-temperature turbine expander is characterized by comprising the following steps of: the method comprises the following steps:
s1, obtaining a meridian plane molded line of a working wheel of a low-temperature turbine expander by a mapping method, and respectively obtaining column coordinate values of each point on a hub line and a wheel cover line based on control point coordinates of the meridian plane molded line;
s2, calculating column coordinate values of a central streamline based on column coordinate values of points on the hub line and the wheel cover line;
s3, taking the column coordinate values of the central streamline as input conditions of the central streamline method, and calculating to obtain the length of the central meridian streamline and the value of the characteristic function through the central streamline method;
and S4, calculating to obtain the theta coordinates of the central meridian line based on the length of the central meridian line and the value of the characteristic function, and obtaining the theta coordinates of the hub line and the wheel cover line, thereby obtaining the central flow surface of the working wheel blade.
2. The method for designing a working wheel of a low temperature turboexpander according to claim 1, wherein the step S1 comprises the steps of:
taking the axial length of the running wheel
B z ＝(0.3-0.4)D 1 (1)
For HUB (HUB) profile:
B z1 ＝B z (2)
for the wheel cover (SHROUD) profile:
B z2 ＝B z -L 1 (4)
in the above, B z1 、B z2 The axial lengths of the meridian hub molded line and the meridian wheel cover molded line are respectively L r1 、L r2 Radial lengths of meridian hub molded line and meridian wheel casing molded line respectively, D 1 Is the diameter of the front edge of the inlet of the working wheel, D' 2 Is the diameter of the tail edge of the wheel cover of the outlet of the working wheel, D' 2 Is the diameter of the tail edge of the outlet hub of the working wheel, L 1 Is the height of the front edge blade of the inlet of the working wheel;
taking meridian hub molded lines as an example, taking the axial length B of the meridian hub molded lines z1 And its radial length L r1 The difference is M equal parts, each equal part length is:
based on M equal parts, respectively with axial length B z1 And radial length L r1 Intersection point O of (2) 0 、O 1 ……、O M As the center of a circle, with radial length L r1 For making a circle with radius, respectively obtaining an arc and an axial length B z1 Intersecting at points 0,1, … …, N, where n=m, then the axial length B will be z1 And radial length L r1 The included angle of (2) is also divided into M equal parts, and the intersection points P of the angular bisectors and the corresponding circular arcs respectively 0 、P 1 、……、P N The control point of the meridian hub molded line is the control point;
thereby obtaining the control point P of the meridian hub molded line N (n=0, 1, …, M) has a coordinate expression of P (z) N ，r N ) Wherein, the method comprises the steps of, wherein,
z N ＝B z -(M-N)a-L r cos(δ N +θ N ) (7)
in the above, z N Is a control point axial columnCoordinate value r N Is the radial column coordinate value delta of the control point N Is a long side B z1 And short side L r1 Angle value, θ after equal division of angle M N Is the center of a circle and the control point P N An included angle between the connecting line and the axial direction;
in combination with the cosine law, equations (7) and (8) are transformed into:
the calculation modes of column coordinate values of the meridian wheel cover molded line and the meridian hub molded line are the same, and the hub molded line and the wheel cover molded line obtained by the control point coordinates of the meridian wheel cover molded line and the meridian hub molded line are the meridian molded line for designing the working wheel of the turbine expander.
3. The method for designing a working wheel of a low temperature turboexpander of claim 2, wherein M in step S1 has a value in the range of 30 to 50.
4. The method for designing a working wheel of a low temperature turboexpander according to claim 2, wherein the step S2 comprises the steps of:
establishing a geometrical relationship between a cylindrical coordinate system (z, r, theta) and a patch orthogonal coordinate system (t, b, n) based on meridian coordinates s: wherein 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 flow line direction of 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 meridian coordinate s is in the z-r plane of a cylindrical coordinate system (z, r, theta);
and obtaining column coordinate values of points on the hub line and the wheel cover line in the z-r plane based on the geometric relationship between the meridian plane and the column coordinate system (z, r, theta) obtained by a mapping method and the body-attached orthogonal coordinate system (t, b, n), and then calculating the column coordinate values of the central streamline, wherein the column coordinate values of the points on the central streamline are obtained by adding the column coordinate values of the points on the corresponding hub line and the wheel cover line and dividing by 2.
5. The method for designing a working wheel of a low temperature turboexpander of claim 4, wherein the step S3 comprises the steps of:
taking the column coordinate value of the central streamline as an input condition of the central streamline method to obtain an axial direction increment dz and a radial direction increment dr between control points on the central streamline, and defining the length sL of the central streamline, wherein the length increment between the control points on the central streamline is as follows:
wherein the length of the central streamline of the inlet of the running wheel is sL1, the length of the central streamline of the outlet of the running wheel is sL2, the length of the central streamline is calculated from the outlet of the running wheel, namely sL2=0, and sL1 is the length increment dsL between the control points on the central streamline of each section added by sL2.
6. The method for designing a working wheel of a low temperature turboexpander of claim 5, wherein the step S3 further comprises the steps of:
and (3) derivation of characteristic functions:
the relative velocity air flow angle β is assumed to satisfy the following relationship:
in the formula (11), K is an index value for controlling the change of the relative velocity air flow angle in the flow channel, C is the difference of the residual values of the inlet and outlet relative velocity air flow angles, and beta 1 Air flow angle representing relative velocity of leading edge of inlet of running wheel, when s L ＝s L2 When=0, β=β 2，mean The method comprises the following steps:
C＝cscβ 2,mean -cscβ 1 (12)
the following steps can be obtained:
wherein beta is 2，mean A relative velocity air flow angle representing the leading edge of the rotor outlet center streamline;
defining a characteristic function:
the geometrical relationship between the cylindrical coordinate system (z, r, θ) and the orthographic coordinate system (t, b, n) of the body can be obtained:
bringing the feature function into availability:
7. the method for designing a working wheel of a low temperature turboexpander of claim 6 wherein in step S3, K has a value in the range of 1 to 20.
8. The method for designing a working wheel of a low temperature turboexpander of claim 6 wherein in step S4, the θ coordinates of the central meridian line are: θmean' =θmean+dθ; the theta coordinates of the wheel cover line and the hub line are: θshroud=θhub=θmean'.
9. The method for designing a working wheel of a low-temperature turboexpander according to any one of claims 1 to 8, further comprising the steps of: and S5, rotating the array through CATIA three-dimensional drawing software to obtain the three-dimensional modeling design of the running wheel.
CN202210723531.8A 2022-06-24 2022-06-24 Design method of working wheel of low-temperature turbine expander Pending CN117332546A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210723531.8A CN117332546A (en) 2022-06-24 2022-06-24 Design method of working wheel of low-temperature turbine expander

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210723531.8A CN117332546A (en) 2022-06-24 2022-06-24 Design method of working wheel of low-temperature turbine expander

Publications (1)

Publication Number Publication Date
CN117332546A true CN117332546A (en) 2024-01-02

Family

ID=89274269

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210723531.8A Pending CN117332546A (en) 2022-06-24 2022-06-24 Design method of working wheel of low-temperature turbine expander

Country Status (1)

Country Link
CN (1) CN117332546A (en)

Similar Documents

Publication Publication Date Title
CN101708559B (en) Five-coordinate plunge milling machining method of closed type bladed disc
CN101149061A (en) Centrifugal impeller suitable for high rotation speed operation
CN113217461B (en) Blade, molding method and manufacturing method thereof and air compressor
CN106446324B (en) Design method of final-stage twisted blade of large industrial steam turbine
CN114722518B (en) Turbine basic blade profile parameterization design method
CN1189666C (en) Efficient propeller with blades curled backward for centrifugal propeller machinery
CN108829970A (en) Axial fan blade optimum design method and optimization system based on vortex dynamics
CN103925244B (en) A kind of big flow high load axial compressor and fan for 300MW F level heavy duty gas turbines
CN111435399A (en) Molding method of fan assembly
CN110657126B (en) Non-axisymmetrical hub structure for controlling flow of centrifugal impeller and centrifugal impeller
CN116220913A (en) Low-loss engine pre-rotation air supply system
CN113958519B (en) Automatic generation method for blades in different shapes of centrifugal impeller based on intermediate surface
CN115952604A (en) Centrifugal impeller blade generation method based on free-form surface blade neutral surface
CN109882446B (en) Design method of low specific speed centrifugal pump impeller splitter blade
CN100370148C (en) Blade type optimized designing method of turbine compression fluid machine
CN114542207A (en) Design method for outer surface modeling of turbine rear casing support plate
CN112160937B (en) Cross-flow fan blade
CN110374928B (en) Design method of tubular diffuser and tubular diffuser
CN113374731A (en) Turbine rotor, expander and air cycle machine
CN117332546A (en) Design method of working wheel of low-temperature turbine expander
CN114444415B (en) Radial flow turbine stator nozzle guide vane design optimization method and system
CN108757568B (en) Axial flow fan blade
Liang et al. The recent progresses in industrial centrifugal compressor designs
CN116186913A (en) Design method of full-parameterized pump-jet propeller
CN113094833B (en) Diffuser design method with dovetail leading edge and radial and axial blade integration

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination