A method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making

Abstract

The present invention relates to a method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making. The gas jet velocity formed by the annular gap nozzle structure optimized by the present invention has slow decay, high jet quality, and high powder yield of the prepared metal powder for 3D printing. The method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making of the present invention comprises the following steps: ① estimation of the maximum Mach number of the annular gap nozzle outlet, ② setting of the initial profile of the expansion section nozzle, ③ estimation of the starting coordinates, ④ optimization of the profile of the supersonic expansion section of the annular gap nozzle, and ⑤ correction of the profile of the supersonic expansion section of the annular gap nozzle. The new atomization nozzle structure designed by the technical solution of the present invention can prepare a powder yield of 60% of the metal powder for 3D printing.

Description

Technical Field

[0001] The invention relates to the field of gas atomization powder making, and in particular to an annular seam profile of a supersonic atomization nozzle, and in particular to an optimization method thereof. Background Art

[0002] With the development of 3D technology, the demand for high-performance metal powder is increasing. Vacuum induction melting gas atomization powder making technology is currently the main method for preparing conventional metal powders. The core component of the atomization nozzle structure determines the key technical indicators of the prepared metal powder, such as particle size distribution, sphericity and satellite powder rate.

[0003] In the actual production process, due to the limitations of the powder making nozzle structure, the powder yield of metal powder in a specific range for the 3D printing process is generally low, resulting in a large amount of recycled powder, which ultimately leads to a sharp increase in production costs and a large waste of energy.

[0004] The key to improving the powdering rate of metal powder for 3D printing is to optimize the structure of the powder making nozzle and improve the gas jet speed and quality of the atomized metal liquid flow. The annular seam flow channel profile structure of the atomizing nozzle is a key factor limiting the gas jet speed and quality, but its specific design method has not been published in the art. Therefore, it is of urgent and important practical significance to provide a supersonic annular seam nozzle profile design method for gas atomization powder making. Summary of the invention

[0005] The purpose of the present invention is to provide a method for optimizing the design of the key position of a supersonic nozzle and the profile of an annular seam nozzle flow channel, so as to ensure that the atomizing nozzle forms a high-quality supersonic gas jet and improve the powdering rate of metal powder in a specific section for preparing 3D printing.

[0006] The present invention provides a method for optimizing the profile of a supersonic annular seam nozzle for gas atomization powder making, which is characterized by comprising the following steps:

[0007] Design a supersonic annular gap nozzle profile consisting of a subsonic annular gap contraction section and a supersonic annular gap expansion section, with a throat as the boundary in the middle; the supersonic annular gap expansion section is composed of a circular arc segment and a power function quadratic curve;

[0008] Estimate the maximum Mach number at the annular nozzle exit;

[0009] The expansion section profile is iteratively optimized using the maximum Mach number in combination with a characteristic line method, wherein the starting position of the characteristic line iteration is a starting line.

[0010] Further preferably, the starting line equation is:

[0011]

[0012] Where γ is the specific heat ratio of the gas in the annular nozzle; a is the local sound speed p is the local air pressure, ρ is the local atmospheric density, L = ρ t +r t , ρ t is the arc radius of the arc segment, r t is the ordinate of the throat.

[0013] Further preferably, the iterative optimization firstly calculates the position (x1, y1) and (x2, y2) of two adjacent points of the starting line and the speed parameter (u x1 ,u y1 )、(u x2 ,u y2 ), calculate the position of the downstream intersection of the characteristic line passing through the two adjacent points and the flow parameters (x3, y3), (u x3 ,u y3 ), which is an iterative interior point unit process.

[0014] Further preferably, the expansion section profile is optimized by sequentially iterating the core area, the uniform area and the turning area R; the Mach number distribution along the X axis in the core area satisfies Ma=Ma(x), the gas is gradually accelerated, and the design Mach number is reached at point K to satisfy Ma=Ma max , point K is the dividing point between the core area and the uniform area; for the uniform area, it is only necessary to determine a line with an angle of α with the X axis at point K. D =sin -1 (1 / M max ) and intersects with the iterative optimization curve at point F, while satisfying the mass flow rate m through the FK line FK Equal to the mass flow rate m through half of the initial line BD ; For the direction-changing area R, in order to ensure uniform airflow velocity in the uniform area, the angle between all left characteristic lines and the X-axis must be α D =sin -1 (1 / M max ), and based on the IK and FK characteristic line conditions obtained by calculation in the first two stages, through the internal point unit process, the corresponding right characteristic line and left characteristic line are issued according to the initial points on KF and IK to satisfy the mass conservation, and the position coordinates of the end points of each characteristic line are determined, thereby realizing the optimization of the expansion section profile.

[0015] Further preferably, the estimation of the maximum Mach number at the outlet of the supersonic expansion section of the annular nozzle specifically comprises the following steps:

[0016] First, given the nozzle inlet total pressure P0, ambient pressure and preset Mach number range, equation (3) is used to iteratively estimate the maximum Mach number Ma corresponding to the outlet pressure P closest to the ambient pressure: max; Then, the estimated Mach number Ma max Substitute into equation (2) to calculate the area ratio A / A*, and then calculate the annular nozzle outlet width based on the input annular nozzle throat size, supersonic expansion section outlet size, subsonic contraction section inlet size, annular nozzle throat distance to the guide tube center length L1 and annular nozzle supersonic expansion section distance to the guide tube center length L2, and determine the nozzle position and exit point coordinates;

[0017]

[0018]

[0019] Where A is the exit cross-sectional area of ​​the supersonic expansion section;

[0020] A* is the cross-sectional area of ​​the annular nozzle throat;

[0021] γ is the specific heat ratio of the gas in the annular nozzle;

[0022] P is the nozzle outlet pressure;

[0023] P0 is the total pressure at the nozzle inlet;

[0024] Ma is the gas Mach number.

[0025] Further preferably, the profile of the supersonic annular gap expansion section is corrected by using the viscous boundary layer correction theory; specifically, the following conditions are met:

[0026] d(x)=xtanα(4)

[0027] where d(x) is the displacement thickness of the boundary layer at point x and α=0.5.

[0028] The beneficial effects of the present invention are: the optimal annular seam airflow channel profile structure of the new atomizing nozzle optimized by the above method significantly improves the quality of the supersonic gas jet and the gas velocity, and the powder formation rate of the prepared metal powder in the range of powder for 3D printing is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are described in detail below.

[0030] Figure 1 The overall structure diagram of the nozzle of the method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making according to the present invention.

[0031] Figure 2 The invention discloses a schematic diagram of an annular gap nozzle profile for optimizing a supersonic annular gap nozzle profile for gas atomization powder making.

[0032] Figure 3 The present invention is an overall optimization flow chart of a method for optimizing a supersonic annular gap nozzle profile for gas atomization powder making.

[0033] Figure 4 The present invention is a diagram showing the calculation principle of the internal points involved in a method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making.

[0034] Figure 5 The invention discloses a method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making, which involves a diagram for determining the parameters of the gas flow field at the outlet of the expansion section.

[0035] Figure 6 The invention discloses a method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making, which relates to a schematic diagram of the optimization principle of the expansion section profile.

[0036] Figure 7 The invention discloses a method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making, and adopts MATLAB software to design the nozzle profile.

[0037] Figure 8 This is a particle size distribution diagram of GH3536 powder prepared by a nozzle structure optimized by a method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making according to the present invention.

[0038] Fig. 9 This is a morphology distribution diagram of GH3536 powder prepared by a nozzle structure optimized by a method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making according to the present invention.

[0039] Among them, 1. guide tube; 2. annular gap nozzle; 3. subsonic contraction section curve of annular gap nozzle; 4. throat curve of annular gap nozzle; 5. supersonic expansion section curve of annular gap nozzle; 6. starting line. DETAILED DESCRIPTION

[0040] Based on the nozzle gas-liquid two-phase flow atomization mechanism, the present invention believes that the key to improving the powder formation rate of the interval section for 3D printing is the nozzle annular seam airflow channel structure, which has the conditions for forming a high-speed and uniformly distributed high-quality gas jet. Therefore, a supersonic annular seam nozzle profile optimization method for gas atomization powder making is proposed. In order to clearly illustrate the specific technical optimization scheme of the implementation method of the present invention, the implementation method is described in detail below in conjunction with the accompanying drawings.

[0041] See also Figures 1 to 9 The following is an explanation.

[0042] See also Figure 1 As shown, the overall structure of the atomizing powder making nozzle includes a guide tube 1 for the metal liquid flow channel, a key part for the formation of the gas jet, and a supersonic annular gap nozzle 2.

[0043] See also Figure 2 As shown, the supersonic annular gap nozzle includes a subsonic contraction section and a supersonic expansion section, and the profile curve includes annular gap nozzle subsonic contraction section curve 3, annular gap nozzle throat curve 4 and annular gap nozzle supersonic expansion section curve 5, and curve 4 and curve 5 constitute the nozzle supersonic section optimization curve.

[0044] The subsonic annular seam contraction section 3 generally adopts a bicubic curve to determine its profile, and the control equation is as follows:

[0045]

[0046] Where x m D is the front and back connection point of the two curves; i is the cross-sectional diameter at the axial distance x, 0.5<x m / L<0.6, D is the initial diameter, which is set between 3-10 mm, wherein x=0 is the starting point of the subsonic annular gap contraction section, and L is the length of the subsonic annular gap contraction section.

[0047] See also Figure 3 As shown in the figure, the optimization process of the supersonic annular gap expansion section includes: ① estimation of the maximum Mach number of the annular gap nozzle outlet, ② setting of the initial profile of the expansion section nozzle, ③ estimation of the starting coordinates, ④ optimization of the supersonic annular gap nozzle expansion section profile, and ⑤ size correction of the nozzle profile.

[0048] The maximum Mach number at the outlet of the supersonic expansion section of the annular nozzle is estimated by using the pseudo-one-dimensional steady isentropic flow formula:

[0049] The Mach number of the nozzle divergence section depends only on the area ratio:

[0050]

[0051] The static pressure in the nozzle expansion section depends only on the Mach number:

[0052]

[0053] Where A is the exit cross-sectional area of ​​the supersonic expansion section;

[0054] A* is the cross-sectional area of ​​the annular nozzle throat;

[0055] γ is the specific heat ratio of the gas in the annular nozzle;

[0056] P is the nozzle outlet pressure;

[0057] P0 is the total pressure at the nozzle inlet;

[0058] Ma is the gas Mach number.

[0059] When designing, the nozzle inlet total pressure P0, ambient pressure and preset Mach number range are first given. The program is written using MATLAB software to iteratively estimate the maximum Mach number Ma corresponding to the outlet pressure P closest to the ambient pressure through equation (3). max Secondly, the estimated Mach number Ma max Substitute into equation (2) to calculate the area ratio A / A*, and then calculate the annular gap nozzle outlet width based on the input annular gap nozzle 2 throat size d2, supersonic expansion section outlet size d3, subsonic contraction section inlet size d1, annular gap nozzle 2 throat distance to the center of the guide tube 1 length L1 and annular gap nozzle 2 supersonic expansion section distance to the center of the guide tube 1 length L2, and preliminarily determine the nozzle position and exit point coordinates.

[0060] To further facilitate the establishment of functions and equations, the oxy coordinate system is defined as follows: the positive direction of the x-axis points along the axis toward the nozzle outlet, the positive direction of the y-axis is vertically upward, and o is the origin of the coordinate system, which is located at the midpoint of the starting line.

[0061] The initial profile of the optimized curve of the expansion section of the annular gap nozzle is assumed to be a combination of the throat arc segment and the quadratic function curve, so that the assumed nozzle profile structure can be solved and optimized by the characteristic line method. The characteristic line equation and compatibility equation are as follows:

[0062]

[0063]

[0064] where u x with u y are the x-axis and y-axis velocity, a is the speed of sound, θ is the flow angle, α is the velocity deviation angle, ± represents the direction of the left and right characteristic lines, du x± With y± They are respectively expressed as the differential of the x-axis component velocity in the direction of the left and right characteristic lines and the differential of the y-axis component velocity in the direction of the left and right characteristic lines.

[0065] See also Figure 2 As shown, arc segment: composed of arc half angle θ and radius ρ t Determine, the estimated design initial value of θ is 15°-45°, ρ t The estimated initial design value is 5-20mm. Quadratic power function curve: y=a+bx+cx 2 To determine the values ​​of coefficients a, b, and c, we need to know: the location of the connection point A (x a ,y a ), connection angle θ a and the outlet edge angle θ e . The position of the connection point A is determined by the following equation:

[0066] xa =ρ t sinθ a； (8)

[0067] y a =r t +(1-cosθ a )ρ t， (9)

[0068] where r t is the ordinate of the throat, and the value of θ is generally 0.3-0.5 mm in gas atomization powder making experiments. a The estimated design initial value is 30°-40°. To ensure uniform gas jet velocity at the annular nozzle outlet, the outlet edge angle θ e The general value is 0°. According to the designed arc radius ρ t , we can determine x a ,y a , and substitute it into the following equation, the coordinates of the expansion section exit position and the edge angle θ e Given that, the coefficients a, b and c can be determined jointly.

[0069] y=a+bx+cx 2 (10)

[0070] tanθ a =b+2cx(11)

[0071] tanθ e =b+2cx(12)

[0072] The initial profile structure of the expansion section was further determined.

[0073] The optimization of the supersonic expansion section of the annular nozzle starts iterating from the starting coordinates. The starting coordinates are estimated by calculating the starting line position 6 using the Sauer method, which is used as the starting value of the iterative calculation of the characteristic line method. The starting line equation is:

[0074]

[0075] Where γ is the specific heat ratio of the gas in the annular nozzle; a is the local sound speed L=ρ t +r t ;

[0076] The starting line speed can be determined by the following formula:

[0077]

[0078]

[0079] Where u x with uy are the velocity components in the x and y directions on the starting line respectively, and a* is the critical sound speed Where T0 = constant, which is the stagnation point temperature; R is the gas constant; is a dimensionless quantity,

[0080]

[0081] The expansion section profile of the supersonic annular gap nozzle is optimized by writing an algorithm using MATLAB software, and the characteristic line method is used to iteratively calculate the core area, uniform area and change direction area R in turn, ultimately achieving the optimization of the expansion section profile structure.

[0082] See also Figure 2 and Figure 4 As shown in the figure, the calculation process of an inner point of the expansion section of the annular nozzle is to first determine the positions (x1, y1), (x2, y2) and velocity parameters (u of two adjacent points 1 and 2 on the starting line 6 according to the estimated starting line position 6. x1 ,u y1 )、(u x2 ,u y2 ). The unit process of the interior point is used to calculate the location of the downstream intersection of the characteristic line passing through points 1 and 2 and the flow parameters (x3, y3), (u x3 ,u y3 ), and the estimation method is used to solve it. The process of using the estimation method is as follows:

[0083] ① Ideal gas sound velocity equation:

[0084]

[0085] After setting the stagnation temperature T according to experience, a=a(u) is obtained, where a is the speed of sound, R is the gas constant, γ is the specific heat ratio of the gas in the annular nozzle, and u is the velocity value.

[0086] ② Use the estimation method to calculate the coefficients. For the estimation method, take the flow parameter u downstream of the characteristic line x± ,u y± ,y ± The values ​​of are equal to their values ​​at points 2 and 1, namely:

[0087] u x+ =u 2x ;u y+ =u 2y ;y + =y2

[0088] u x- =u 1x ;u y- =u 1y ;y - =y1

[0089] Substituting into the following equation, we can get the speed value u ± , flow angle θ ± , speed of sound a ± , Mach number Ma ± , speed deviation angle α ± .

[0090]

[0091]

[0092] a ± =a(V ± )(18)

[0093]

[0094]

[0095] Then θ ± , a ± ,Ma ± , α ± Substitute into the following equation

[0096] λ ± =tan(θ±α) (21)

[0097] Q ± =u x± 2 -a ± 2 (twenty two)

[0098]

[0099]

[0100] Where λ, Q, N and S are intermediate variables.

[0101] Determine x3, y3, u by estimation x3 and u y3 . Substitute the above calculated values ​​into the following equation and solve for x3 and y3.

[0102] y3-λ + x3=y2-λ + x2 (25)

[0103] y3-λ - x3=y1-λ - x1 (26)

[0104] Based on the values ​​solved previously, solve T according to the following equation ± .

[0105] T + =S - (x3-x2)+Q + u 2x +N + u 2y (27)

[0106] T - =S - (x3-x1)+Q - u 1x +N + u 1y (28)

[0107] According to the solved Q ± 、N ± 、T ± Substitute into the following equation to solve for u 3x ,u 3y

[0108] Q + u 3x +N + u 3y =T + (29)

[0109] Q - u 3x +N - u 3y =T - (30)

[0110] At this point, the iterative calculation of the position coordinates and velocity of an inner point in the expansion segment has been completed.

[0111] See also Figure 5 As shown, the Mach number distribution along the X axis in the core area satisfies Ma=Ma(x), the gas gradually accelerates, and reaches the design Mach number at point K, satisfying Ma=Ma max . IK indicates the generation of Ma max The flow parameters of the IK line can be determined by interpolation based on the flow parameter values ​​on the two right characteristic lines upstream and downstream.

[0112] Then, the gas velocity in the uniform zone of the annular nozzle is required to be parallel and uniform, so a line α D =sin -1 (1 / M max ) angle straight characteristic line extends from point K to downstream point F. At the same time, the mass flow rate m through the FK line must be satisfied FK Equal to the mass flow rate m through half of the initial line BD .

[0113] See also Figure 6 As shown in Figure 1, the remaining part is the iterative calculation in the turning area R and the final optimization of the expansion section profile. To ensure that the speed in the uniform area is uniform and parallel, all left characteristic lines and X

[0114] The angle between the axes must satisfy α D =sin -1 (1 / M max ); Based on the calculations in the first two stages, IK and FK are obtained

[0115] Under the characteristic line conditions, through the internal point unit iteration process, the corresponding right characteristic line and left characteristic line are issued according to the initial points on FK and IK to satisfy the mass conservation of the airflow, and the position coordinates of the end points of each characteristic line are determined, thereby obtaining each new quadratic function line IF wall point to achieve the expansion section surface optimization.

[0116] The surface correction of the supersonic expansion section of the annular gap nozzle adopts the viscous boundary layer correction theory to correct the wall coordinates. The viscous boundary layer correction theory is:

[0117] Assume that the displacement thickness of the boundary layer develops linearly with the axis, satisfying d(x) = xtanα. Since the ambient pressure of the powder atomizing nozzle is designed to be atmospheric pressure, the outlet Mach number is ≤4, and α is finally set to 0.5.

[0118] d(x) is the boundary layer displacement thickness at point x;

[0119] α represents the linear correction angle;

[0120] Mach number of test section 1.5～4 6 8 10 α / (°) 0.5 0.7 1.5 2.0

[0121] See also Figure 7 As shown, the MATLAB program algorithm designed by the patented technical solution is used to optimize the surface structure of the supersonic expansion section of the annular gap nozzle.

[0122] See also Figure 8 and Fig. 9 As shown, the atomizing nozzle with the annular seam flow channel profile structure designed by the patented technical solution, argon gas is selected as the atomizing gas, and the main spray pressure is 4MPa, the prepared GH3536 original powder D 50 =31μm, achieving the goal of a powder formation rate of up to 60% in the 3D printing range. At the same time, the prepared alloy powder has high sphericity and extremely low satellite powder rate.

Claims

1. A method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making, characterized in that The following steps are involved: Design a supersonic annular gap nozzle profile consisting of a subsonic annular gap contraction section and a supersonic annular gap expansion section, with a throat as the boundary in the middle; the supersonic annular gap expansion section is composed of a circular arc segment and a power function quadratic curve; Estimate the maximum Mach number at the annular nozzle exit; Iteratively optimizing the expansion section profile using the maximum Mach number in combination with the characteristic line method, wherein the starting position of the characteristic line iteration is the starting line; The equation of the starting line is: Where γ is the specific heat ratio of the gas in the annular nozzle, a is the local sound speed p is the local air pressure, ρ is the local atmospheric density, L = ρ t +r t , ρ t is the arc radius of the arc segment, r t is the ordinate of the throat; The iterative optimization first calculates the position of two adjacent points on the starting line (x1, y1), (x2, y2) and the speed parameter (u x1 ,u y1 )、(u x2 ,u y2 ), calculate the position (x3, y3) of the downstream intersection of the characteristic line passing through the two adjacent points and the flow parameters (u x3 ,u y3 ), thus completing the iterative estimation of the core area, uniform area and turning area R in the expansion section in turn, and the iterative optimization process is an interior point unit process.

2. The method for optimizing the profile of a supersonic annular seam nozzle for gas atomization powder making according to claim 1, characterized in that: The optimization of the expansion section profile is carried out by gradually iterating the core area, uniform area and turning area R in sequence; the Mach number distribution along the X axis in the core area satisfies Ma=Ma(x), the gas is gradually accelerated, and at point K, the designed Mach number satisfies Ma=Ma max , point K is the dividing point between the core area and the uniform area; for the uniform area, it is only necessary to determine a line with an angle of α with the X axis at point K. D =sin -1 (1 / M max ) and intersects with the iterative optimization curve at point F, while satisfying the mass flow rate m through the FK line FK Equal to the mass flow rate m through half of the initial line BD ; For the turning area R, the angle between all left characteristic lines and the X axis must be α D =sin -1 (1 / M max ), under the known IK and KF characteristic line conditions, through the internal point unit process, the corresponding right characteristic line and left characteristic line are issued according to the initial points on KF and IK to satisfy the mass conservation of the airflow, and the position coordinates of the end points of each characteristic line are determined, thereby realizing the optimization of the expansion section profile.

3. The method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making according to claim 1, characterized in that: The estimation of the maximum Mach number at the outlet of the supersonic expansion section of the annular nozzle specifically includes the following steps: First, given the nozzle inlet total pressure p0, ambient pressure and preset Mach number range, equation (3) is used to iteratively estimate the maximum Mach number Ma corresponding to the outlet pressure p closest to the ambient pressure: max ; Then, the estimated Mach number Ma max Substitute the Ma parameter in equation (2) to calculate the area ratio A / A*, and then calculate the annular nozzle outlet width based on the input annular nozzle throat size, supersonic expansion section outlet size, subsonic contraction section inlet size, annular nozzle throat distance from the guide tube center length L1 and annular nozzle supersonic expansion section distance from the guide tube center length L2, and determine the nozzle position and exit point coordinates; Where A is the exit cross-sectional area of ​​the supersonic expansion section; A* is the cross-sectional area of ​​the annular nozzle throat; γ is the specific heat ratio of the gas in the annular nozzle; p is the nozzle outlet pressure; p0 is the total pressure at the nozzle inlet; Ma is the gas Mach number.

4. The method for optimizing the profile of a supersonic annular gap nozzle for gas atomization powder making according to claim 1, characterized in that: The viscous boundary layer correction theory is used to correct the profile of the supersonic annular gap expansion section; specifically, the following conditions are met: d(x)=xtanα (4) where d(x) is the displacement thickness of the boundary layer at point x and α=0.5(°).

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