Bezier curve-based streamline variable-diameter scroll pipe separator and design method

Abstract

The application discloses a streamline variable-diameter scroll pipe separator based on a Bezier curve and a design method thereof. The separator comprises a scroll pipe, a spiral blade and a main flow pipe. The profile line of the scroll pipe is composed of three parts, namely, an air inlet section, a separation section and a sand discharge section. The profile line of the air inlet section is a straight line, and the profile lines of the separation section and the sand discharge section are Bezier curves. The spiral blade is arranged in the scroll pipe. The scroll pipe, the spiral blade and the main flow pipe are coaxially arranged. The plane where the end of the air inlet section of the scroll pipe is located is aligned with the air inlet end surface of the spiral blade. The profile line of the spiral blade is the same as the profile line of the separation section of the scroll pipe. One end of the main flow pipe extends into the sand discharge section of the scroll pipe. A distance is kept between the end surface of the main flow pipe and the air outlet end surface of the spiral blade. The application can improve the sand and dust separation efficiency, reduce the sudden change in the scroll pipe, reduce the local resistance loss and optimize the aerodynamic performance of the scroll pipe separator.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of gas-solid separator, and particularly relates to a streamline variable-diameter vortex tube separator based on a Bezier curve and a design method. BACKGROUND

[0002] The vortex tube separator is a new type of axial guide vane cyclone separator, has the advantages of small flow loss, high separation efficiency, high gas treatment efficiency, small unit volume and convenient layout, and is therefore widely used in the industrial fields of aviation, shipbuilding, metallurgy and the like, and military industrial products such as helicopter intake protection and warship gas turbine intake filter.

[0003] The main components of the vortex tube separator include a spiral blade, a vortex tube and a main flow tube. When the vortex tube separator works, air flows into the separator, and a rotating air flow field is generated in the vortex tube under the action of the spiral blade. In the rotating air flow field, solid particles with a large density are subjected to a large inertial centrifugal force, and therefore fly to the wall surface of the circular tube in a spiral motion with a large trajectory radius. After the particles collide with the wall surface of the circular tube, the particles lose the initial speed and perform spiral motion with the air flow near the wall surface, and are discharged through a sand discharge channel. The air and a small number of particles not captured flow out from the main flow tube at the center position, so that the separation and purification effect is achieved. At present, the research on the vortex tube separator is mostly concentrated on the optimization of basic structural parameters such as the modification of the rear edge of the central body, the twist angle of the blade, the inlet diameter of the main flow tube, the length of the separator and the length of the spiral blade channel, and no relevant research is performed on the optimization of the separation efficiency and the aerodynamic performance from the main structure of the spiral blade and the vortex tube. SUMMARY

[0004] The present application aims at the problems in the prior art, and provides a streamline variable-diameter vortex tube separator based on a Bezier curve and a design method, which optimizes the separation efficiency and the aerodynamic performance from the main structure of the spiral blade and the vortex tube, can improve the sand dust separation efficiency, reduce the sudden change in the vortex tube, reduce the local resistance loss, and optimize the aerodynamic performance of the vortex tube separator.

[0005] In order to achieve the above object, the present application has the following technical scheme:

[0006] The application discloses a streamlined variable-diameter vortex tube separator based on a Bezier curve, which comprises a vortex tube, a spiral blade and a main flow tube; the profile line of the vortex tube is composed of three parts, namely, an air inlet section, a separation section and a sand discharge section, wherein the profile line of the air inlet section is a straight line, and the profile lines of the separation section and the sand discharge section are Bezier curves; the spiral blade is arranged in the vortex tube, the vortex tube, the spiral blade and the main flow tube are coaxially arranged, the plane where the air inlet end of the vortex tube is located is aligned with the air inlet end surface of the spiral blade, the profile line of the spiral blade is the same as the profile line of the separation section of the vortex tube, and the end surface of the main flow tube is kept a distance from the air outlet end surface of the spiral blade.

[0007] As a preferred scheme, the Bezier curve adopted by the profile line of the spiral blade and the profile line of the separation section of the vortex tube has the following characteristics:

[0008] The starting point and the ending point of the Bezier curve coincide with the starting point and the ending point of the corresponding characteristic polygon;

[0009] The tangent direction at the starting point and the ending point of the Bezier curve is consistent with the trend of the first side and the last side of the characteristic polygon;

[0010] All the points on the Bezier curve fall in the convex hull formed by the control points P i .

[0011] As a preferred scheme, the profile line of the air inlet section of the vortex tube is determined according to the following expression:

[0012]

[0013] In the formula, z is the axial coordinate position of the air inlet section of the vortex tube, y is the y-direction coordinate of the section of the air inlet section of the vortex tube, theta is the air inlet angle, x is the x-direction coordinate of the section of the air inlet section of the vortex tube, r0 is the inner radius of the tail part of the air inlet section, L in is the length of the air inlet section.

[0014] As a preferred scheme, the profile line of the separation section of the vortex tube is a third-order Bezier curve, and the coordinates of the four control points are expressed in the following matrix:

[0015]

[0016] The expression of the third-order Bezier curve formed is as follows:

[0017] C gs (u)=(1-u) 3 P gs0 +3u(1-u) 2 P gs1 +3u 2 (1-u)P gs2+u 3 P gs3 ,u∈[0,1]

[0018] The expression of the x coordinate and the z coordinate in the third-order Bezier curve is obtained from the third-order Bezier curve expression as follows:

[0019]

[0020] In the formula, P gs is a coordinate matrix of the control points of the separation section, x gs0 , x gs1 , x gs2 , and x gs3 are the x coordinates of the control point 0, the control point 1, the control point 2, and the control point 3 of the separation section respectively, z gs0 , z gs1 , z gs2 , and z gs3 are the z coordinates of the control point 0, the control point 1, the control point 2, and the control point 3 of the separation section respectively, r0 is the inner radius of the tail of the inlet section, L in is the length of the inlet section, Δl1 is the distance between the first control point and the second control point of the separation section, Δl2 is the distance between the third control point and the fourth control point of the separation section, θ is the inlet angle, α is the variable-diameter coefficient, γ is the sand discharge angle, L is the length of the separation section, C gs (u) is the Bezier curve of the separation section, u is the parameter range, and the value is 0-1, P gw0 , P gw1 , P gw2 , and P gw3 are the coordinates of the control point 0, the control point 1, the control point 2, and the control point 3 of the separation section respectively, x gw (u) is the x coordinate under the value u of the separation section, z gw (u) is the z coordinate under the value u of the separation section, x i is the x coordinate of the i control point of the separation section, z i is the z coordinate of the i control point of the separation section, and i is the i control point, and the value is 0-3.

[0021] As a preferred scheme, the sand discharge section profile line of the scroll pipe is a third-order Bezier curve, and the coordinates of the four control points are expressed in the following matrix:

[0022]

[0023] The expression of the third-order Bezier curve formed is as follows:

[0024] C gw (u)=(1-u) 3 P gw0 +3u(1-u) 2 P gw1 +3u2 (1-u)P gw2 +u 3 P gw3 ,u∈[0,1]

[0025] The expression of x coordinate and z coordinate in the cubic Bezier curve is obtained from the expression of the cubic Bezier curve as follows:

[0026]

[0027] In the formula, P gw is the coordinate matrix of the control points of the sand discharge section, x gw0 , x gw1 , x gw2 , x gw3 are respectively the x coordinates of the control point 0, the control point 1, the control point 2 and the control point 3 of the sand discharge section, z gw0 , z gw1 , z gw2 , z gw3 are respectively the z coordinates of the control point 0, the control point 1, the control point 2 and the control point 3 of the sand discharge section, α is the variable diameter coefficient, r0 is the inner radius of the tail pipe of the air inlet section, L in is the length of the air inlet section, L is the length of the separation section, Δl3 is the distance between the first control point and the second control point of the sand discharge section, Δl4 is the distance between the third control point and the fourth control point of the sand discharge section, γ is the sand discharge angle, β is the air discharge angle, L out is the length of the sand discharge section, C gw (u) is the Bezier curve of the sand discharge section, u is the parameter range and has a value of 0-1, P gw0 , P gw1 , P gw2 , P gw3 are respectively the coordinates of the control point 0, the control point 1, the control point 2 and the control point 3 of the sand discharge section, x gw (u) is the x coordinate under the value u of the sand discharge section, z gw (u) is the z coordinate under the value u of the sand discharge section, x i is the x coordinate of the i control point of the sand discharge section, z i is the z coordinate of the i control point of the sand discharge section, i is the i control point and has a value of 0-3.

[0028] As a preferred scheme, the first derivative of the inlet section, the separation section and the sand discharge section of the scroll tube profile line is continuous; for the connection between the inlet section and the separation section, the first derivative of the inlet section profile line is:

[0029] z′=-tanθ,

[0030] the first derivative of the separation section profile line is:

[0031]

[0032] In the formula, z′ is the first derivative of the intake section profile, θ is the intake angle, and x gs ′(0) is the first derivative of the x-coordinate when the value of u in the separation segment is 0, z gs ′(0) is the first derivative of the z-coordinate when the u value of the separation section is 0, and Δl1 is the distance between the first control point and the second control point of the separation section; make the first derivative of the intake section profile line equal to the first derivative of the separation section profile line to achieve the continuity of the first derivative at the connection between the intake section and the separation section;

[0033] At the junction of the separation section and the sand discharge section, the first derivative of the separation section outline is:

[0034]

[0035] The first derivative of the sand discharge section outline is:

[0036]

[0037] In the formula, x gs ′(1) is the first derivative of the x-coordinate when the value of u in the separation segment is 1, z gs ′(1) is the first derivative of the z-coordinate when the value of u in the separation segment is 1, Δl2 is the distance between the third and fourth control points in the separation segment, γ is the sand discharge angle, and x gw ′(0) is the first derivative of the x-coordinate when the value of u in the sand discharge section is 0, z gw ′(0) is the first derivative of the z-coordinate when the u value of the sand discharge section is 0, and Δl3 is the distance between the first control point and the second control point of the sand discharge section; make Δl2=Δl3 to realize the continuity of the first derivative at the connection between the separation section and the sand discharge section.

[0038] A design method for a streamlined variable-diameter vortex separator based on Bézier curves includes the following steps:

[0039] Determine the end face profile and radius of the helical blade;

[0040] Construct a three-dimensional coordinate system;

[0041] Determine the diameter coefficient α, inlet angle θ, sand discharge angle γ, and exhaust angle β of the streamlined variable diameter vortex separator based on the Bezier curve;

[0042] The inlet section, separation section, and sand discharge section of the vortex tube profile are constructed based on the diameter variation coefficient α, inlet angle θ, sand discharge angle γ, and exhaust angle β of the streamlined variable diameter vortex tube separator based on the Bézier curve. The profile of the inlet section is a straight line, while the profiles of the separation section and the sand discharge section are Bézier curves. The profile of the helical blade is the same as the profile of the separation section of the vortex tube.

[0043] The vortex tube, the spiral blade and the main flow tube are assembled, the vortex tube, the spiral blade and the main flow tube are coaxially arranged, and the plane where the gas inlet section of the vortex tube ends is aligned with the gas inlet end surface of the spiral blade, one end of the main flow tube is inserted by the sand discharging section of the vortex tube, and a distance is kept between the end surface of the main flow tube and the gas outlet end surface of the spiral blade.

[0044] As a preferred scheme, in the step of constructing the three-dimensional coordinate system, the three-dimensional coordinate system is constructed at the gas inlet end surface of the vortex tube, the XY plane is fixed on the plane where the gas inlet end surface is located, the origin position is located at the central position of the gas inlet end surface, and the Z axis is perpendicular to the XY plane.

[0045] As a preferred scheme, in the step of determining the variable-diameter coefficient α, the gas inlet angle θ, the sand discharging angle γ and the gas outlet angle β of the vortex tube separator based on the Bezier curve, the ratio of the radius r0 of the connection between the gas inlet section and the separation section of the vortex tube to the radius r1 of the connection between the separation section and the sand discharging section of the vortex tube 1 is defined as the variable-diameter coefficient α; the angle between the inlet of the vortex tube and the horizontal direction is defined as the gas inlet angle θ, the angle between the direction vector at the terminal point of the contour line of the spiral blade and the horizontal direction is defined as the sand discharging angle γ, and the angle between the direction vector at the terminal end of the vortex tube and the positive direction of the X axis is defined as the gas outlet angle β.

[0046] Compared with the prior art, the vortex tube separator based on the Bezier curve has at least the following beneficial effects:

[0047] When the gas inlet angle θ is greater than 0°, the vortex tube separator based on the Bezier curve can increase the gas inlet area, thereby improving the gas inlet efficiency and accelerating the separation speed of the gas and the sand dust; the separation section of the vortex tube and the spiral blade are designed based on the Bezier curve, so that the separation efficiency can be improved, the abrupt change in the vortex tube can be reduced, and the airflow loss caused by the sharp point can be reduced to a certain extent. The vortex tube separator based on the Bezier curve has great geometric flexibility, is simple in structure, can effectively improve the sand dust separation efficiency and the aerodynamic performance of the vortex tube separator, and can be widely applied to occasions where the separation of sand dust and gas is required, such as helicopters. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 The three-dimensional coordinate system constructed at the gas inlet end surface of the vortex tube of the embodiment of the present application is shown in the schematic diagram.

[0049] Figure 2 The contour line of the vortex tube of the embodiment of the present application is composed of three parts, i.e., the gas inlet section, the separation section and the sand discharging section, as shown in the schematic diagram.

[0050] Figure 3 The characteristic parameter position of the vortex tube separator based on the Bezier curve of the embodiment of the present application is shown in the schematic diagram.

[0051] Figure 4 This is a schematic diagram of the vortex tube outline and control points according to an embodiment of the present invention;

[0052] Figure 5 This is a schematic diagram of the outline of the helical blade in an embodiment of the present invention;

[0053] Figure 6 This is a three-dimensional structural diagram of a streamlined variable-diameter vortex tube separator based on Bezier curves, according to an embodiment of the present invention. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0055] Please see Figure 6 This invention proposes a streamlined variable-diameter vortex separator based on Bézier curves, comprising a vortex tube 1, a helical blade 2, and a main flow tube 3. For example... Figure 2 As shown, the contour of the vortex tube 1 consists of three parts: an intake section, a separation section, and a sand discharge section. The contour of the intake section is a straight line, while the contours of the separation section and the sand discharge section are Bezier curves. The spiral blade 2 is located inside the vortex tube 1. The vortex tube 1, the spiral blade 2, and the main flow pipe 3 are coaxially arranged. The plane at the end of the intake section of the vortex tube 1 is aligned with the intake end face of the spiral blade 2. The contour of the spiral blade 2 is the same as the contour of the separation section of the vortex tube 1. One end of the main flow pipe 3 extends into the sand discharge section of the vortex tube 1, and the end face of the main flow pipe 3 maintains a distance from the exhaust end face of the spiral blade 2.

[0056] Furthermore, this embodiment of the invention also proposes a design method for the streamlined variable diameter vortex tube separator based on Bézier curves, specifically including the following steps:

[0057] Step 1: Determine the end face profile of the helical blade 2 and its radius r0;

[0058] Step 2: Construct a three-dimensional coordinate system based on the end face profile of the propeller blade. The center of the end face profile is taken as the origin of the coordinate system, and the plane containing this origin is the XY plane. The planes perpendicular to this origin are the XZ plane and the YZ plane, respectively. Figure 1 As shown;

[0059] Step 3: Determine the diameter variation coefficient α, inlet angle θ, sand discharge angle γ, and exhaust angle β of the streamlined variable diameter vortex separator based on Bézier curves. The definitions of each parameter are as follows: Figure 2 , 3 As shown;

[0060] Step Four: As Figure 4As shown, the profile line of the spiral blade 2 and the Bezier curve of the separation section of the vortex tube 1 are the same, and the profile line of the vortex tube 1 is constructed based on the determined variable-diameter coefficient α, the air inlet angle θ, the sand discharge angle γ and the air outlet angle β.

[0061] As shown in step five, the vortex tube 1, the spiral blade 2 and the main flow tube 3 are assembled, the end of the air inlet section of the vortex tube 1 is aligned with the air inlet end surface of the spiral blade 2, and the main flow tube 3 is kept a distance from the air outlet end surface of the spiral blade 2; the vortex tube 1, the spiral blade 2 and the main flow tube 3 are coaxially arranged. Figure 5 、 6 As shown in step five, the vortex tube 1, the spiral blade 2 and the main flow tube 3 are assembled, the end of the air inlet section of the vortex tube 1 is aligned with the air inlet end surface of the spiral blade 2, and the main flow tube 3 is kept a distance from the air outlet end surface of the spiral blade 2; the vortex tube 1, the spiral blade 2 and the main flow tube 3 are coaxially arranged.

[0062] The profile line of the spiral blade 2 and the profile line of the separation section of the vortex tube 1 adopt the Bezier curve, which has the following characteristics:

[0063] The starting point and the ending point of the Bezier curve coincide with the starting point and the ending point of the corresponding characteristic polygon;

[0064] The tangent direction at the starting point and the ending point of the Bezier curve is consistent with the trend of the first side and the last side of the characteristic polygon;

[0065] The points on the Bezier curve all fall within the convex hull formed by the control points P i .

[0066] The above-mentioned characteristic polygon is composed of the connecting dotted lines of the control points of the Bezier curve, as shown in Figure 4 .

[0067] In step three, the radius of the connection between the air inlet section and the separation section of the vortex tube 1 is defined as r0, the radius of the connection between the separation section and the sand discharge section of the vortex tube 1 is defined as r1, and the ratio of the two is the variable-diameter coefficient α. The angle between the inlet of the vortex tube 1 and the horizontal direction is defined as the air inlet angle θ, the angle between the direction vector at the end of the profile line of the spiral blade 2 and the horizontal direction is defined as the sand discharge angle γ, and the angle between the direction vector at the end of the vortex tube 1 and the positive direction of the X-axis is defined as the air outlet angle β.

[0068] In step four, the vortex tube 1 is composed of three parts: the air inlet section, the separation section and the sand discharge section. The profile line of the air inlet section is a straight line; in order to reduce the resistance loss, the profile lines of the separation section and the sand discharge section all adopt the Bezier curve, and the first-order derivative is continuous.

[0069] The length of the air inlet section of the vortex tube is defined as L in , and the expression of the air inlet section curve in the coordinate system is:

[0070]

[0071] The length of the vortex tube separation section is denoted as L, and a third-order Bezier curve is used, so four control points are needed. The coordinates of the four control points are denoted as P gs0 (x gs0 ,z gs0 ), P gs1 (x gs1 ,z gs1 ), P gs2 (x gs2 ,z gs2 ), and P gs3 (x gs3 ,z gs3 ), respectively, to obtain a third-order Bezier curve of the profile line, wherein P gs0 (x gs0 ,z gs0 ) and P gs3 (x gs3 ,z gs3 ) are end points, and P gs1 (x gs1 ,z gs1 ) and P gs2 (x gs2 ,z gs2 ) are intermediate control points. Here, the distance between the first control point and the second control point is Δl1, and the distance between the third control point and the fourth control point is Δl2, both of which are positive numbers. Therefore, the Bezier curve control point matrix of the separation section can be expressed as follows:

[0072]

[0073] The Bezier curve equation formed is as follows:

[0074] C gs (u)=(1-u) 3 P gs0 +3u(1-u) 2 P gs1 +3u 2 (1-u)P gs2 +u 3 P gs3 ,u∈[0,1]

[0075] The expressions of the x coordinate and the z coordinate in the third-order Bezier curve are obtained from the parametric equation of the third-order Bezier curve as follows:

[0076]

[0077] The first derivative of the above third-order Bezier curve is as follows:

[0078]

[0079] The length of the vortex tube sand discharge section is denoted as Lout A third order Bezier curve is used, thus four control points are needed, and the coordinates of the four control points are respectively P gw0 (x gw0 ,z gw0 ), P gw1 (x gw1 ,z gw1 ), P gw2 (x gw2 ,z gw2 ) and P gw3 (x gw3 ,z gw3 ), wherein P gw0 (x gw0 ,z gw0 ) and P gw3 (x gw3 ,z gw3 ) are end points, and P gw1 (x gw1 ,z gw1 ) and P gw2 (x gw2 ,z gw2 ) are intermediate control points, and the distance between the first control point and the second control point is Δl3, and the distance between the third control point and the fourth control point is Δl4, both of which are positive numbers. Thus, the Bezier curve control point matrix of the sand discharge section can be expressed as follows:

[0080]

[0081] The Bezier curve equation formed is as follows:

[0082] C gw (u)=(1-u) 3 P gw0 +3u(1-u) 2 P gw1 +3u 2 (1-u)P gw2 +u 3 P gw3 ,u∈[0,1]

[0083] The expressions of the x coordinate and the z coordinate in the third order Bezier curve are obtained from the parametric equation of the third order Bezier curve as follows:

[0084]

[0085] The first order derivative of the above third order Bezier curve is as follows:

[0086]

[0087] The three curves are connected in sequence to form the outline of the scroll pipe, and to ensure the smoothness of the outline, the first derivative continuity needs to be ensured, and only the derivative continuity at the two connecting points needs to be considered here.

[0088] For the connection between the inlet section and the separation section, the first derivative of the inlet section outline is:

[0089] z' = -tanθ

[0090] The first derivative of the separation section outline is:

[0091]

[0092] They are equivalent, that is, the derivative continuity at the connection between the inlet section and the separation section.

[0093] For the connection between the separation section and the discharge section, the first derivative of the separation section outline is:

[0094]

[0095] The first derivative of the discharge section outline is:

[0096]

[0097] To ensure that they are equal, only Δl2= Δl3 is required.

[0098] Through verification, compared with the traditional scroll pipe separator, the new scroll pipe separator designed by the method of the application has an improved separation efficiency of 0-1.55% for sand dust with a particle size in the range of 3-27 microns, a reduced resistance loss of 173-517 Pa, an improved separation efficiency of 0-0.45% for sand dust with a particle size of more than 27 microns, and a reduced resistance loss of 84-263 Pa under the given working conditions. It is proved that the design method of the flow line variable diameter scroll pipe separator based on the Bezier curve is feasible.

[0099] The above-described embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for some technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A flowline variable diameter scroll tube separator based on a Bezier curve, characterized by: The utility model relates to a vortex tube (1), spiral blade (2) and main flow pipe (3), the profile line of vortex tube (1) is by intake section, separation section and sand discharge section three parts, wherein, the profile line of intake section is a straight line, the profile line of separation section and sand discharge section is Bezier curve, spiral blade (2) is arranged in the inside of vortex tube (1), vortex tube (1), spiral blade (2) and main flow pipe (3) are coaxial arrangement, and the plane where the end of intake section of vortex tube (1) is located is aligned with the air inlet end surface of spiral blade (2), the profile line of spiral blade (2) is same with the profile line of separation section of vortex tube (1), one end of main flow pipe (3) is inserted by sand discharge section of vortex tube (1), and the end surface of main flow pipe (3) and the exhaust end surface of spiral blade (2) keep a distance. The profile line of separation section of vortex tube (1) is three order Bezier curve, and the coordinates of four control points are expressed as the following matrix: The three order Bezier curve expression formed is: The expression of x coordinate and z coordinate in three order Bezier curve is obtained from three order Bezier curve expression: In the formula, is the coordinate matrix of the control points of the separation section, , , , are respectively the x coordinates of the control point 0, the control point 1, the control point 2 and the control point 3 of the separation section, , , , are respectively the z coordinates of the control point 0, the control point 1, the control point 2 and the control point 3 of the separation section, is the inner radius of the tail pipe of the inlet section, is the length of the inlet section, is the distance between the first control point and the second control point of the separation section, is the distance between the third control point and the fourth control point of the separation section, is the inlet angle, is the variable-diameter coefficient, is the sand discharge angle, is the length of the separation section, is the Bezier curve of the separation section, is the parameter range, the value is 0~1, , , , are respectively the coordinates of the control point 0, the control point 1, the control point 2 and the control point 3 of the separation section, is the x coordinate under the u value of the separation section, is the z coordinate under the u value of the separation section, is the x coordinate of the control point of the separation section , is the z coordinate of the control point of the separation section , is the control point , the value is 0~3; The profile line of sand discharge section of vortex tube (1) is three order Bezier curve, and the coordinates of four control points are expressed as the following matrix: The three order Bezier curve expression formed is: The expression of x coordinate and z coordinate in three order Bezier curve is obtained from three order Bezier curve expression: In the formula, is the coordinate matrix of the control points of the sand discharge section, , , , is the x coordinate of the control point 0, the control point 1, the control point 2, and the control point 3 of the sand discharge section respectively, , , , is the z coordinate of the control point 0, the control point 1, the control point 2, and the control point 3 of the sand discharge section respectively, is the variable diameter coefficient, is the inner radius of the tail pipe of the air inlet section, is the length of the air inlet section, is the length of the separation section, is the distance between the first control point and the second control point of the sand discharge section, is the distance between the third control point and the fourth control point of the sand discharge section, is the sand discharge angle, is the exhaust angle, is the length of the sand discharge section, is the Bezier curve of the sand discharge section, is the parameter range, the value is 0~1, , , , is the coordinate of the control point 0, the control point 1, the control point 2, and the control point 3 of the sand discharge section respectively, is the x coordinate under the u value of the sand discharge section, is the z coordinate under the u value of the sand discharge section, is the x coordinate of the control point of the sand discharge section, is the z coordinate of the control point of the sand discharge section, is the control point of the sand discharge section, is the control point of the sand discharge section, is the control point, the value is 0~3.

2. The flowline variable diameter scroll pipe separator based on Bezier curves of claim 1, wherein, The profile line of spiral blade (2) and the Bezier curve of the profile line of separation section of vortex tube (1) have the following characteristics: The starting point and the terminal point of Bezier curve coincide with the starting point and the terminal point of the corresponding characteristic polygon; The tangent direction at the starting point and the terminal point of Bezier curve is consistent with the trend of the first side and the last side of the characteristic polygon; The points on the Bezier curve all fall within the convex hull formed by the Bezier curve control points The convex hull formed by the Bezier curve control points 3. The flowline variable diameter scroll pipe separator based on Bezier curves of claim 1, wherein, The profile line of intake section of vortex tube (1) is determined according to the following expression: wherein is an axial coordinate position of the scroll tube intake section, is a y coordinate of the cross section of the scroll tube intake section, is an intake angle, is an x coordinate of the cross section of the scroll tube intake section, is an inner radius of the intake section tail, is an intake section length.

4. The flowline variable diameter scroll pipe separator based on Bezier curves of claim 1, wherein, The first derivative of the profile line of intake section, separation section and sand discharge section of vortex tube (1) is continuous; For the connection of intake section and separation section, the first derivative of the profile line of intake section is: ， The first derivative of the profile line of separation section is: wherein is the first derivative of the profile line of the inlet section, is the inlet angle, is the first derivative of the x coordinate at the u value of 0 of the separation section, is the first derivative of the z coordinate at the u value of 0 of the separation section, is the distance between the first control point and the second control point of the separation section; the first derivative of the profile line of the inlet section is equal to the first derivative of the profile line of the separation section, so that the first derivative at the connection of the inlet section and the separation section is continuous. For the connection of separation section and sand discharge section, the first derivative of the profile line of separation section is: The first derivative of the profile line of sand discharge section is: wherein, is the first derivative of the x coordinate at the separation segment with u = 1, is the first derivative of the z coordinate at the separation segment with u = 1, is the distance between the third and fourth control points of the separation segment, is the sand discharge angle, is the first derivative of the x coordinate at the sand discharge segment with u = 0, is the first derivative of the z coordinate at the sand discharge segment with u = 0, is the distance between the first and second control points of the sand discharge segment; and is the first derivative of the x coordinate at the sand discharge segment with u = 0, 5. A method of designing a Bezier curve based flow streamlined variable diameter scroll pipe separator according to any one of claims 1 to 4, characterized in that, The utility model relates to the following steps: Determine the end surface profile line of spiral blade (2) and radius; Construct three-dimensional coordinate system; Determining a variable diameter coefficient for the variable diameter scroll tube separator based on a Bezier curve , an inlet angle , a sand discharge angle , and an exhaust angle ; Variable diameter coefficient of the variable-diameter scroll pipe separator based on Bezier curve , inlet angle , sand discharge angle , and exhaust angle The inlet section, separation section and sand discharge section of the profile line of the scroll pipe (1) are constructed; wherein the profile line of the inlet section is a straight line, and the profile lines of the separation section and the sand discharge section are Bezier curves; the profile line of the spiral blade (2) is the same as the profile line of the separation section of the scroll pipe (1); Assemble vortex tube (1), spiral blade (2) and main flow pipe (3), and vortex tube (1), spiral blade (2) and main flow pipe (3) are coaxial arrangement, and the plane where the end of intake section of vortex tube (1) is located is aligned with the air inlet end surface of spiral blade (2), one end of main flow pipe (3) is inserted by sand discharge section of vortex tube (1), and the end surface of main flow pipe (3) and the exhaust end surface of spiral blade (2) keep a distance.

6. The method of designing according to claim 5, wherein, In the step of constructing three-dimensional coordinate system, construct three-dimensional coordinate system at the air inlet end surface of vortex tube (1), fix XY plane in the plane where the air inlet end surface is located, and the original point position is located at the center position of the air inlet end surface, and Z axis is perpendicular to XY plane.

7. The method of designing according to claim 5, wherein, The diameter variation coefficient of the streamlined variable diameter vortex separator based on the Bezier curve was determined. Intake angle , sand discharge angle and exhaust angle In the steps, the radius of the connection between the inlet section and the separation section of the vortex tube (1) is defined as... The radius of the connection between the separation section and the sand discharge section of vortex tube 1 is The ratio of the two is the diameter coefficient. The angle between the inlet of the vortex tube (1) and the horizontal direction is defined as the intake angle. The angle between the direction vector at the end of the profile of the helical blade (2) and the horizontal direction is the sand discharge angle. The angle between the direction vector at the end of the vortex tube (1) and the positive X-axis is the exhaust angle. .

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