A two-dimensional nozzle profile design method with side offset and two-dimensional nozzle

Abstract

The invention discloses a two-dimensional nozzle profile design method with a lateral offset and a two-dimensional nozzle. The two-dimensional nozzle profile design method comprises: obtaining a cross-sectional equation of the two-dimensional nozzle at any position x along the flow direction, and determining the cross-sectional area at the position x; obtaining initial design parameters of the two-dimensional nozzle, and respectively calculating the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction; determining the center line of the two-dimensional nozzle based on the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction; obtaining the two-dimensional nozzle profile based on the cross-sectional area at the position x and the center line of the two-dimensional nozzle; the method of the present application reduces the lateral force on the nozzle wall with a lateral offset, thereby making up for the deficiency of the research on the two-dimensional nozzle profile with respect to the lateral offset in the prior art.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft exhaust system design, and more specifically, relates to a two-dimensional nozzle profile design method with side offset and a two-dimensional nozzle. Background Art

[0002] With the development of infrared remote sensing detection technology, infrared guided missiles have gradually become one of the major threats to modern UAVs, and the development of infrared stealth technology has become an urgent need to improve the battlefield survivability of modern UAVs. The infrared radiation of aircraft mainly comes from the skin and exhaust system; when Ma<2.0, 90% of the infrared radiation of aircraft comes from the exhaust system, and the working band of the infrared guided missile seeker in service is mainly 3-5μm. Therefore, suppressing the infrared radiation of aircraft in the 3-5μm band is of great significance to improving the battlefield survivability of aircraft.

[0003] The tail jet of an aircraft is the main infrared radiation source of the exhaust system. Since its front, side and rearward detection range is wide, suppressing its infrared radiation is a very important issue. The use of a dual nozzle is an important measure to suppress the infrared radiation intensity of the exhaust system. At the same time, the dual nozzle has certain advantages in thrust vector integration, reducing infrared and radar cross-section characteristic signals and full life cycle costs. Currently, most of the stealth drones in service use dual nozzles (F-117, B-2, X-47B, RQ-180). The infrared radiation of the dual nozzle has obvious non-axisymmetric characteristics. The infrared radiation intensity in the direction corresponding to the narrow side is small, and the infrared radiation intensity in the direction corresponding to the wide side is slightly larger. Studies have shown that the radiation intensity of the thermal jet of the dual nozzle is 30% to 50% lower than that of the circular nozzle.

[0004] At present, the design equations of two-dimensional circle-to-square nozzle profile are divided into two categories: curvature and super ellipse control equations. The curvature control method is mostly used in the design of the inlet profile, and the nozzle profile mostly adopts the super ellipse control equation. The super ellipse design method includes the cross-sectional shape design and the variation law of the cross-sectional control parameters along the process. Due to the internal space limitations of UAVs, the turbine end face and the nozzle outlet section often have longitudinal and lateral offsets. The current design method can achieve the longitudinal offset, and the design method for the lateral offset is relatively rare.

[0005] Therefore, it is expected to invent a two-dimensional nozzle profile design method that can make up for the shortcomings of the existing technology in the research on the lateral offset of the two-dimensional nozzle profile. Summary of the invention

[0006] The purpose of the present invention is to provide a two-dimensional nozzle profile design method to make up for the deficiency of the two-dimensional nozzle profile research on lateral offset in the prior art.

[0007] In order to achieve the above object, the present invention provides a method for designing a two-dimensional nozzle profile with a side offset, wherein the inlet cross section of the two-dimensional nozzle is circular and the outlet cross section is rectangular, comprising:

[0008] Step 1: Obtain a cross-sectional equation of the binary nozzle at any position x along the flow direction;

[0009] Step 2: Determine the cross-sectional area of ​​the position x according to the cross-sectional equation of the position x;

[0010] Step 3: Obtaining initial design parameters of the two-dimensional nozzle, and based on the initial design parameters of the two-dimensional nozzle, respectively calculating the variation law of the cross-section control parameters along the flow direction, the variation law of the cross-section control parameters along the lateral direction, and the variation law of the cross-section control parameters along the longitudinal direction;

[0011] Step 4: determining the center line of the binary nozzle based on the variation law of the cross-section control parameter along the flow direction, the variation law of the cross-section control parameter along the lateral direction, and the variation law of the cross-section control parameter along the longitudinal direction;

[0012] Step 5: Based on the cross-sectional area at the position x and the center line of the two-dimensional nozzle, a two-dimensional nozzle profile is obtained.

[0013] Optionally, the cross section of the binary nozzle at any position x along the flow direction is a superellipse, and the cross section equation is

[0014]

[0015] Wherein, y and z are the coordinates of any point on the cross section, a is the major axis radius of the cross section, b is the minor axis radius of the cross section, and η is the variable index of the cross section.

[0016] Optionally, the cross-sectional area is

[0017]

[0018] in, Satisfy t>0;

[0019] Optionally, the step 3 includes:

[0020] Get the initial design parameters of the binary nozzle, which include the inlet cross-sectional coordinate x0 along the flow direction, the inlet cross-sectional area S in , lateral inlet section coordinate y0, longitudinal inlet section coordinate z0, outlet section area S e and nozzle length L;

[0021] Based on the inlet cross-sectional area S in , apply the first formula to obtain the inlet cross-sectional radius R in , and based on the outlet cross-sectional area Se , the second and third formulas are used to obtain the outlet cross-sectional width W d and outlet section height h;

[0022] Based on the two-dimensional nozzle inlet cross-sectional radius R in , determine the inlet section control parameter P in , and based on the outlet cross-sectional width W d and the outlet section height h, determine the outlet section control parameter P e ;

[0023] Based on the inlet cross-section control parameter P in , the outlet section control parameter P e , the inlet section coordinate x0 along the stream direction, the inlet section coordinate y0 along the lateral direction, the inlet section coordinate z0 along the longitudinal direction and the nozzle length L, calculate the variation law of the section control parameters along the stream direction P(x), the variation law of the section control parameters along the lateral direction P(y) and the variation law of the section control parameters along the longitudinal direction P(z) respectively.

[0024] Optionally, the first formula is:

[0025]

[0026] The second formula is:

[0027]

[0028] The third formula is:

[0029]

[0030] Among them, η e is the outlet section variable index, and AR is the outlet section width-to-height ratio.

[0031] Optionally, the variation rule of the cross-section control parameter along the flow direction is:

[0032]

[0033] The lateral variation law of the cross-section control parameters is:

[0034]

[0035] The longitudinal variation law of the cross-section control parameter is:

[0036]

[0037] in, is a function of the relative position of the cross section (x-x0) / L, is a function of the relative position of the cross section (y-y0) / L, It is a function of the relative position of the cross section (z-z0) / L.

[0038] Optionally, i1=(x-x0) / L, i2=(y-y0) / L and i3=(z-z0) / L are set respectively, and the first constraint condition, the second constraint condition and the third constraint condition are determined respectively, wherein the first constraint condition is that i1 is continuous in the interval 0-1, and The second constraint condition is that i2 is continuous in the range of 0-1, and The third constraint condition is that i3 is continuous in the interval 0-1, and

[0039] Based on the first constraint, is constructed into a fifth-order polynomial, based on the second constraint condition, is constructed into a fifth-order polynomial, based on the third constraint, Constructed into a quintic polynomial, where

[0040]

[0041]

[0042]

[0043] Among them, c 51 、c 41 、c 52 、c 42 、c 53 and c 43 Typical value.

[0044] A two-dimensional nozzle with a side offset, wherein the inlet cross section of the two-dimensional nozzle is circular and the outlet cross section is rectangular, and the side offset of the two-dimensional nozzle is calculated using the two-dimensional nozzle profile design method with a side offset.

[0045] The beneficial effects of the present invention are:

[0046] The two-dimensional nozzle profile design method of the present invention first determines the cross-sectional area at the position x according to the cross-sectional equation at the position x, and then, based on the obtained initial design parameters of the two-dimensional nozzle, respectively calculates the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction, and determines the center line of the two-dimensional nozzle based on the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction, and finally obtains the two-dimensional nozzle profile based on the cross-sectional area at the position x and the center line of the two-dimensional nozzle; the two-dimensional nozzle profile design method of the present application reduces the lateral force on the nozzle wall with lateral offset, thereby making up for the deficiency of the research on the lateral offset of the two-dimensional nozzle profile in the prior art.

[0047] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0049] Figure 1 A flow chart of a method for designing a two-dimensional nozzle profile with a side offset according to an embodiment of the present invention is shown;

[0050] Figure 2 A schematic diagram of the structure of a nozzle profile curve family of a two-dimensional nozzle profile design method with side offset according to an embodiment of the present invention is shown, and a profile is generated by connecting and smoothing;

[0051] Figure 3 A schematic diagram of the structure of a nozzle profile curve family according to a two-dimensional nozzle profile design method in the prior art is shown;

[0052] Figure 4 A two-dimensional nozzle positive triaxial measurement diagram showing a two-dimensional nozzle profile design method with side offset according to an embodiment of the present invention;

[0053] Figure 5 A two-dimensional nozzle is shown with a three-axis view of a nozzle profile curve family according to a two-dimensional nozzle profile design method in the prior art;

[0054] Figure 6 A top view of a two-dimensional nozzle is shown according to a two-dimensional nozzle profile design method with side offset according to an embodiment of the present invention;

[0055] Figure 7 A top view of a two-dimensional nozzle showing a nozzle profile curve family according to a two-dimensional nozzle profile design method of the prior art;

[0056] Figure 8 A side view of a two-dimensional nozzle is shown according to a two-dimensional nozzle profile design method with side offset according to one embodiment of the present invention;

[0057] Fig. 9 A side view of a two-dimensional nozzle is shown showing a nozzle profile curve family according to a two-dimensional nozzle profile design method in the prior art. DETAILED DESCRIPTION

[0058] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0059] According to a method for designing a two-dimensional nozzle profile with a side offset of the present invention, the inlet cross section of the two-dimensional nozzle is circular and the outlet cross section is rectangular, comprising:

[0060] Step 1: Obtain the cross-sectional equation of the binary nozzle at any position x along the flow direction;

[0061] Step 2: Determine the cross-sectional area at position x based on the cross-sectional equation at position x;

[0062] Step 3: Obtain the initial design parameters of the two-dimensional nozzle, and based on the initial design parameters of the two-dimensional nozzle, calculate the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction;

[0063] Step 4: Determine the center line of the two-dimensional nozzle based on the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction;

[0064] Step 5: Based on the cross-sectional area at position x and the centerline of the two-dimensional nozzle, the two-dimensional nozzle profile is obtained.

[0065] Specifically, the two-dimensional nozzle profile design method of the present invention first determines the cross-sectional area of ​​the position x according to the cross-sectional equation of the position x, and then, based on the obtained initial design parameters of the two-dimensional nozzle, calculates the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction, and determines the center line of the two-dimensional nozzle based on the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction, and finally, based on the cross-sectional area at position x and the center line of the two-dimensional nozzle, calculates the two-dimensional nozzle profile; the two-dimensional nozzle profile design method of the present application makes up for the deficiencies in the prior art in the research on the lateral offset of the two-dimensional nozzle profile.

[0066] Furthermore, in order to make the two-dimensional convergent nozzle designed based on the super-elliptical cross-section have high aerodynamic performance, it is necessary to design and control the variation law of the nozzle cross-section control parameters along the way.

[0067] Assuming that the nozzle cross-section control parameter is p, the distribution law of parameter p along the nozzle axial direction (x-axis) is expressed by function p(x). Then, when the inlet and outlet cross-section control parameter values ​​are known (assuming that the inlet cross-section control parameter value is pin and the outlet cross-section control parameter value is pe), the variation law of parameter p along the process p(x) can be expressed as the following interpolation function form:

[0068]

[0069] in, is a function of the relative position of the cross section (x-x0) / L, is a function of the relative position of the cross section (y-y0) / L, It is a function of the relative position of the cross section (z-z0) / L.

[0070] Given the nozzle inlet and outlet cross-sectional geometric parameters (inlet and outlet cross-sectional areas, outlet aspect ratio, etc.) and nozzle length, a super ellipse is used to describe the cross-sectional shape of the binary convergent nozzle, and the inlet and outlet cross-sectional parameters are all known.

[0071] In one example, the cross section of a binary nozzle at any position x along the flow direction is a superellipse, and the cross section equation is

[0072]

[0073] Among them, y and z are the coordinates of any point on the cross section, a is the major axis radius of the cross section, b is the minor axis radius of the cross section, and η is the variable index of the cross section.

[0074] In one example, the cross-sectional area is

[0075]

[0076] in, Satisfy t>0;

[0077] Specifically, γ is a generalized integral with parameter t, and gamma is defined.

[0078] In one example, step 3 includes:

[0079] Get the initial design parameters of the two-dimensional nozzle, including the inlet section coordinates x0 along the flow direction, the inlet cross-sectional area S in , lateral inlet section coordinate y0, longitudinal inlet section coordinate z0, outlet section area S e and nozzle length L;

[0080] Based on the inlet cross-sectional area S in , apply the first formula to obtain the inlet cross-sectional radius R in , and based on the outlet cross-sectional area S e , the second and third formulas are used to obtain the outlet cross-sectional width W d and outlet section height h;

[0081] Based on the two-dimensional nozzle inlet cross-sectional radius R in , determine the inlet section control parameter P in , and based on the outlet cross-sectional width W d and the outlet section height h, determine the outlet section control parameter P e ;

[0082] Based on the inlet section control parameter P in , outlet section control parameter P e , the inlet section coordinate x0 along the stream direction, the inlet section coordinate y0 along the lateral direction, the inlet section coordinate z0 along the longitudinal direction and the nozzle length L, calculate the variation law of the section control parameters along the stream direction P(x), the variation law of the section control parameters along the lateral direction P(y) and the variation law of the section control parameters along the longitudinal direction P(z) respectively.

[0083] In one example, the first formula is:

[0084]

[0085] The second formula is:

[0086]

[0087] The third formula is:

[0088]

[0089] Among them, η e is the outlet section variable index, and AR is the outlet section width-to-height ratio.

[0090] In one example, the variation law of the cross-section control parameters along the flow direction is:

[0091]

[0092] The variation law of the cross-section control parameters along the lateral direction is:

[0093]

[0094] The variation law of cross-section control parameters along the longitudinal direction is:

[0095]

[0096] in, is a function of the relative position of the cross section (x-x0) / L, is a function of the relative position of the cross section (y-y0) / L, It is a function of the relative position of the cross section (z-z0) / L.

[0097] In one example, i1=(x-x0) / L, i2=(y-y0) / L, and i3=(z-z0) / L are set respectively, and the first constraint condition, the second constraint condition, and the third constraint condition are determined respectively. The first constraint condition is that i1 is continuous in the interval 0-1, and The second constraint is that i2 is continuous in the range 0-1. and The third constraint is that i3 is continuous in the range 0-1. and

[0098] Based on the first constraint, Constructed into a quintic polynomial, based on the second constraint, Constructed into a quintic polynomial, based on the third constraint, Constructed into a quintic polynomial, where

[0099]

[0100]

[0101]

[0102] Among them, c 51 、c 41 、c 52 、c 42 、c 53 and c 43 Typical value.

[0103] Specifically, Constructed into a quintic polynomial, based on the second constraint, Constructed into a quintic polynomial, based on the third constraint, Constructed into a quintic polynomial, where

[0104]

[0105]

[0106]

[0107] Among them, c 51 、c 41 、c 52 、c 42 、c 53 and c 43 is a typical value. In actual operation, C 51 =6, C 41 =-15, C 52 =-4,C 42 =15, C 53 =-4, C 43 =5.

[0108] A two-dimensional nozzle with a side offset has a circular inlet section and a rectangular outlet section. The side offset of the two-dimensional nozzle is calculated using the two-dimensional nozzle profile design method with the side offset.

[0109] Example 1

[0110] like Figure 1 As shown, a method for designing a two-dimensional nozzle profile with a side offset, wherein the inlet cross section of the two-dimensional nozzle is circular and the outlet cross section is rectangular, comprises:

[0111] Step 1: Obtain the cross-sectional equation of the binary nozzle at any position x along the flow direction;

[0112] Step 2: Determine the cross-sectional area at position x based on the cross-sectional equation at position x;

[0113] Step 3: Obtain the initial design parameters of the two-dimensional nozzle, and based on the initial design parameters of the two-dimensional nozzle, respectively calculate the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction;

[0114] Step 4: Determine the center line of the two-dimensional nozzle based on the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction;

[0115] Step 5: Based on the cross-sectional area at position x and the centerline of the two-dimensional nozzle, the two-dimensional nozzle profile is obtained.

[0116] The specific implementation is:

[0117] Figure 2 The schematic diagram of the structure of the nozzle profile curve family of a two-dimensional nozzle profile design method with side offset according to an embodiment of the present invention is shown, and the profile is generated by connecting the smoothing, Figure 3 The structure diagram of the nozzle profile curve family according to the binary nozzle profile design method of the prior art is shown. Figure 4 A two-dimensional nozzle positive triaxial measurement diagram showing a two-dimensional nozzle profile design method with side offset according to an embodiment of the present invention is shown. Figure 5 A two-dimensional nozzle triaxial diagram showing a nozzle profile curve family according to a two-dimensional nozzle profile design method in the prior art is shown. Figure 6 A top view of a two-dimensional nozzle is shown according to a two-dimensional nozzle profile design method with side offset according to an embodiment of the present invention. Figure 7 A top view of a two-dimensional nozzle showing a nozzle profile curve family according to a two-dimensional nozzle profile design method in the prior art is shown, Figure 8 A side view of a two-dimensional nozzle is shown according to a two-dimensional nozzle profile design method with a side offset according to an embodiment of the present invention. Fig. 9 A side view of a two-dimensional nozzle of a nozzle profile curve family according to a two-dimensional nozzle profile design method of the prior art is shown; by comparing the two-dimensional nozzle obtained by the design method of the present invention with the two-dimensional nozzle obtained by the method of the prior art, it can be seen that, compared with the two-dimensional nozzle without lateral offset, the lateral force on the wall of the nozzle with lateral offset accounts for 13.5% of the total thrust and is directed outward. The nozzle outlet cross-section is a supersonic flow, and a symmetrical double nozzle layout is adopted, so there are two outward forces, and it is necessary to strengthen the connection and fixation of the installation section of the engine and the nozzle to prevent the nozzle from being pushed outward.

[0118] Specifically, structured grid calculation is adopted, and the nozzle inlet is set as the pressure inlet, the outlet as the pressure outlet, the adiabatic no-slip wall, the density-based solver, and the air components are N2, O2, H2O, and CO2; taking the design of a certain cruise point as an example, the total temperature and total pressure of the inner and outer ducts, the ambient atmospheric temperature and pressure are given; the standard k-ωSST turbulence model is adopted, the near-wall area is processed by the standard wall function, the solution is implicit, the convection term is in Roe format, and the flow field has the second-order upwind accuracy.

[0119] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for designing a two-dimensional nozzle profile with a side offset, wherein the inlet cross section of the two-dimensional nozzle is circular and the outlet cross section is rectangular, and the method is characterized in that: include: Step 1: Obtain a cross-sectional equation of the binary nozzle at any position x along the flow direction; Step 2: Determine the cross-sectional area of ​​the position x according to the cross-sectional equation of the position x; Step 3: Obtaining initial design parameters of the two-dimensional nozzle, and based on the initial design parameters of the two-dimensional nozzle, respectively calculating the variation law of the cross-sectional control parameters along the flow direction, the variation law of the cross-sectional control parameters along the lateral direction, and the variation law of the cross-sectional control parameters along the longitudinal direction; Step 4: determining the center line of the binary nozzle based on the variation law of the cross-sectional control parameter along the flow direction, the variation law of the cross-sectional control parameter along the lateral direction, and the variation law of the cross-sectional control parameter along the longitudinal direction; Step 5: Obtaining a binary nozzle profile based on the cross-sectional area at the position x and the center line of the binary nozzle; The cross section of the binary nozzle at any position x along the flow direction is a superellipse, and the cross section equation is: Wherein, y and z are the coordinates of any point on the cross section, a is the radius of the major axis of the cross section, b is the radius of the minor axis of the cross section, and η is the variable index of the cross section; Wherein, the step 3 comprises: Get the initial design parameters of the binary nozzle, which include the inlet cross-sectional coordinate x0 along the flow direction, the inlet cross-sectional area S in , lateral inlet section coordinate y0, longitudinal inlet section coordinate z0, outlet section area S e and nozzle length L; Based on the inlet cross-sectional area S in , apply the first formula to obtain the inlet cross-sectional radius R in , and based on the outlet cross-sectional area S e , the second and third formulas are used to obtain the outlet section width W d and outlet section height h; Based on the two-dimensional nozzle inlet cross-sectional radius R in , determine the inlet section control parameter P in , and based on the outlet cross-sectional width W d and the outlet section height h, determine the outlet section control parameter P e ; Based on the inlet cross-section control parameter P in , the outlet section control parameter P e , the inlet section coordinate x0 along the stream direction, the inlet section coordinate y0 along the lateral direction, the inlet section coordinate z0 along the longitudinal direction and the nozzle length L, respectively calculate the variation law of the section control parameter along the stream direction P(x), the variation law of the section control parameter along the lateral direction P(y) and the variation law of the section control parameter along the longitudinal direction P(z); Among them, the variation law of the cross-section control parameter along the flow direction is: The lateral variation law of the cross-section control parameters is: The longitudinal variation law of the cross-section control parameter is: in, is a function of the relative position of the cross section (x-x0) / L, is a function of the relative position of the cross section (y-y0) / L, It is a function of the relative position of the cross section (z-z0) / L.

2. The method for designing a two-dimensional nozzle profile with a side offset according to claim 1, characterized in that: The cross-sectional area is in, For t>0, γ is a generalized integral with parameter t.

3. The method for designing a two-dimensional nozzle profile with a side offset according to claim 1, characterized in that: The first formula is: The second formula is: The third formula is: Among them, η e is the outlet section variable index, and AR is the outlet section width-to-height ratio.

4. The method for designing a two-dimensional nozzle profile with a side offset according to claim 1, characterized in that: Set i1 = (x-x0) / L, i2 = (y-y0) / L and i3 = (z-z0) / L respectively, and determine the first constraint condition, the second constraint condition and the third constraint condition respectively. The first constraint condition is that i1 is continuous in the interval 0-1, and The second constraint condition is that i2 is continuous in the range of 0-1, and The third constraint condition is that i3 is continuous in the interval 0-1, and Based on the first constraint, is constructed into a fifth-order polynomial, based on the second constraint condition, is constructed into a fifth-order polynomial, based on the third constraint, Constructed into a quintic polynomial, where Among them, c 51 、c 41 、c 52 、c 42 、c 53 and c 43 Typical value.

5. A two-dimensional nozzle with side offset, characterized in that: The inlet cross section of the two-dimensional nozzle is circular, and the outlet cross section is rectangular, and the side offset of the two-dimensional nozzle is calculated using the two-dimensional nozzle profile design method with side offset according to any one of claims 1-4.

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