A method for characterizing roughness in a hole based on an autocorrelation function and modeling a gas film hole

Abstract

This invention discloses a method for characterizing the roughness inside air film pores and inversely modeling air film pores based on autocorrelation functions. The method involves performing CT scanning on air film pores obtained from additive manufacturing to obtain the surface coordinates of the actual rough air film pores; using an ellipsoidal rough structure to simulate complex rough surfaces; and utilizing autocorrelation functions to obtain the simulated rough surface with ellipsoidal protrusions. Rq , ε and λ; ε The value of is related to the actual rough surface. ε The results show that the simulated rough surface parameters are consistent with those of the real rough surface. Rq , ε and λ The invention utilizes a nonlinear multivariate function minimization function fmincon to perform a global search and optimization, thereby obtaining a simulated rough surface that matches the real rough surface. After obtaining the square simulated rough surface, it is mapped onto the inner surface of the film cooling hole. This invention uses simple geometry to fully characterize the complex rough morphology features inside the film cooling hole, and achieves similar film cooling performance to a real rough film cooling hole.

Description

Technical Field

[0001] This invention belongs to the field of gas turbine engine film pore design, specifically involving a method for characterizing the roughness inside the pore and modeling the film pore based on autocorrelation function. Background Technology

[0002] With the development of aero-engines, the temperature of the turbine inlet gas is constantly increasing, which brings serious high-temperature problems. Currently, the growth in demand for increasing turbine inlet temperature consistently outpaces the development of high-temperature resistance properties of blade materials. Therefore, while continuing to develop high-temperature resistant materials and thermal barrier coatings, the exploration of advanced cooling technologies remains indispensable, and film cooling is an important component of advanced turbine cooling structures.

[0003] Currently, various shapes of film cooling orifices have been applied to turbine cooling. However, due to limitations in traditional machining methods, they do not differ significantly in structure from traditional circular orifices. With the continuous development of additive manufacturing, the design of advanced film cooling structures has gained greater freedom. However, additive manufacturing film cooling orifices face problems such as orifice shrinkage and surface roughness. While orifice shrinkage can be corrected through compensation design and external surface roughness can be removed through grinding and polishing, it is difficult to perform internal surface treatment on small and complex film cooling orifice channels. This makes the internal roughness of the orifice a significant factor affecting the flow and heat transfer characteristics of additive manufacturing film cooling orifices.

[0004] Unlike the roughness produced by traditional machining, metal additive manufacturing employs a heating-melting-solidification process for metal powder. This results in both large-scale rough structures and micro-scale surface roughness within the additively manufactured holes. Therefore, the original equivalent uniform roughness of gravel cannot accurately represent the roughness characteristics within the holes. The challenge lies in how to fully characterize the complex roughness morphology within film pores using simple geometric shapes, and how to make it similar to the film cooling performance of real rough film pores. Summary of the Invention

[0005] To address the problem that the roughness inside air film pores caused by additive manufacturing is difficult to characterize using the traditional equivalent gravel uniform roughness, the purpose of this invention is to provide a method for characterizing the roughness inside the pores and modeling air film pores based on autocorrelation functions. This method uses simple geometry to fully characterize the complex roughness features inside the air film pores and achieves similar air film cooling performance to real rough air film pores.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A method for characterizing the roughness inside a pore and modeling air film pores based on an autocorrelation function is characterized by the following specific steps:

[0008] Step 1: Perform CT scanning on the air film pores obtained from additive manufacturing to obtain the coordinates of the actual rough air film pore surface. Represent the air film pore surface coordinates within a square using coordinate transformation and interpolation. Utilize the autocorrelation function to obtain the three corresponding autocorrelation characteristic parameters: 1. Height R of the central peak. AC (0,0), which is numerically equal to the root mean square height Rq of the roughness; 2. The distance λ between the two protrusions, which is the basic wavelength of the rough structure; 3. The aspect ratio of the central peak protrusion, i.e., the average roughness element eccentricity ε.

[0009] The autocorrelation function in this invention is in the form of:

[0010]

[0011]

[0012] In the formula, x and z are the two coordinate axes of the plane, and Y(x,z) represents the surface roughness height at the (x,z) coordinate. Δx represents the average value of all roughness heights on the surface, Δx and Δz represent the coordinate differences between points on the plane, and the sign function distinguishes the peaks and valleys of the surface.

[0013] Step 2: Employ an ellipsoidal roughness structure to simulate complex rough surfaces. First, randomly generate hemispherical protrusions of different diameters on the surface. Then, use the following formula to transform the hemispherical protrusions into an ellipsoidal distribution:

[0014] a i =F D ·D i

[0015]

[0016]

[0017]

[0018] Among them, D i Let F be the diameter of a randomly generated hemisphere of different diameters, ε be the eccentricity of the random rough element, and F be the diameter of the hemisphere of different diameters. D F is the diameter scaling factor. X Let be the scaling factor in the x-direction. For any set of ε, F D and F X Any value of can produce a simulated rough surface with ellipsoidal protrusions.

[0019] Step 3: Use the autocorrelation function to obtain the autocorrelation image of the simulated rough surface with ellipsoidal protrusions in Step 2, from which three autocorrelation parameters Rq, ε and λ can be obtained.

[0020] Step 4: To obtain a simulated rough surface that matches the real rough surface Rq, ε, and λ, the value of ε should match that of the real rough surface. And F D and F X The values ​​are used to perform a global search and optimization using the fmincon function in the MATLAB Optimization Toolbox to obtain a simulated rough surface that matches the real rough surface Rq,ε and λ.

[0021] Step 5: After obtaining the square simulated rough surface, it is mapped onto the inner surface of the film air hole. First, the simulated rough structure is mapped to the coordinate system of the cylindrical film air hole through coordinate transformation and interpolation to obtain the coordinate point cloud data of the inner surface of the film air hole. The point cloud data is divided into several groups according to the direction perpendicular to the inner axis of the hole, and each group of point clouds is imported into NX software and spline curves are formed respectively. Finally, a cylindrical surface with an ellipsoidal simulated rough morphology is established in NX software using several spline curves. This cylindrical surface is the simulated rough inner surface of the film air hole established in this invention.

[0022] The beneficial effects of this invention are:

[0023] Traditional methods for characterizing the roughness of uniform gravel are insufficient to represent the complex rough morphology features within the air film pores of additive manufacturing. This invention uses an autocorrelation function to extract three morphology distribution characteristic parameters of the rough surface, and uses a simple semi-ellipsoidal structure to generate a simulated rough morphology surface that matches the characteristic parameters of the real rough surface. Through reverse modeling and numerical simulation, it is verified that the air film cooling characteristics of the simulated rough air film pore inner surface generated by the algorithm of this invention using a simple semi-ellipsoidal structure are comparable to the air film cooling performance of the real rough air film pore inner surface. This realizes the function of characterizing the flow heat transfer characteristics of complex rough morphologies with simple geometry, which is conducive to carrying out systematic research on the flow heat transfer characteristics of rough structures within the air film pores of additive manufacturing. Attached Figure Description

[0024] Figure 1 A schematic diagram of a real rough surface.

[0025] Figure 2 Autocorrelation results image of a real rough surface.

[0026] Figure 3 Distribution diagram of the initial hemispherical rough element.

[0027] Figure 4 The simulated rough surface generated in this invention.

[0028] Figure 5 This is a schematic diagram illustrating how the three autocorrelation parameters Rq, ε, and λ are obtained using the autocorrelation function in this invention.

[0029] Figure 6 Autocorrelation results image of simulated rough surface.

[0030] Figure 7 The implementation method generates 101 sets of spline curves.

[0031] Figure 8 The air film pores corresponding to the rough surface obtained by reverse modeling.

[0032] Figure 9 Distribution cloud maps of cooling efficiency of real rough film air pores and simulated rough film air pores.

[0033] Figure 10 Lateral average cooling efficiency distribution diagrams of real rough film cooling holes and simulated rough film cooling holes.

[0034] Figure 11 Cooling efficiency distribution at the centerline of a real rough film air hole, a simulated rough film air hole, and a classic smooth circular hole. Detailed Implementation

[0035] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0036] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0037] A method for characterizing the roughness inside pores and modeling air film pores based on autocorrelation functions, the specific steps of which are as follows:

[0038] Step 1: Perform CT scanning on the air film pores obtained by additive manufacturing to obtain the parameters of the real rough surface, and use the autocorrelation function to obtain the corresponding three autocorrelation characteristic parameters.

[0039] As attached Figure 1 As shown, an additively manufactured air film pore model is subjected to CT scanning to obtain the surface roughness distribution, which is denoted as the real rough surface.

[0040] As attached Figure 2 As shown, data from real rough surfaces are substituted into the autocorrelation function formula for data analysis to obtain the autocorrelation results for the real rough surfaces. The autocorrelation function formula is:

[0041]

[0042]

[0043] The autocorrelation surface characteristics of this simulated surface are as follows: Rq = 0.041, ε = 1.333, λ = 1.4751

[0044] Step 2: This invention uses an ellipsoidal rough structure to simulate complex rough surfaces.

[0045] As attached Figure 3 The diagram shows the initial hemispherical rough element distribution generated by this invention. Ten points are taken in both the x and z directions, forming a 10×10 point set, with each point serving as the center of the hemisphere. A random value is generated for each point according to a normal distribution, and this random value is used as the radius of the sphere centered at that point. The random values ​​follow a normal distribution, with a maximum value not exceeding 0.5. After drawing the spheres, if two spheres intersect, the maximum radius of the intersecting region is taken.

[0046] After generating the hemispherical raised rough surface, the following three parameters are used to correct the rough element: 1) the eccentricity ε of the random rough element, 2) the diameter scaling factor F. D 3) Scaling factor F in the x-direction X The following formula can be used to transform the resulting hemispherical protrusions into an ellipsoidal distribution.

[0047] a i =F D ·D i

[0048]

[0049]

[0050]

[0051] Among them, D i Let F be the diameter of a randomly generated hemisphere of different diameters, ε be the eccentricity of the random rough element, and F be the diameter of the hemisphere of different diameters. D F is the diameter scaling factor. X Let be the scaling factor in the x-direction. For any set of ε, F D and F X Any value of can produce a simulated rough surface with ellipsoidal protrusions.

[0052] As attached Figure 4 As shown, this is a simulated rough surface after stretching and scaling the hemispherical protrusion in this invention. The characteristic parameters of this simulated rough surface are consistent with the characteristic parameters of the real rough surface.

[0053] Step 3: Use the autocorrelation function to obtain the autocorrelation image of the simulated rough surface with ellipsoidal protrusions from Step 2. From this image, three autocorrelation parameters Rq, ε, and λ can be obtained, as shown in the attached figure. Figure 5 As shown, where ε = a / b.

[0054] Step 4: In Step 2, Di represents the diameter of randomly generated hemispheres of different diameters, where F... D and FX The values ​​are used to perform a global search and optimization using the fmincon function in the MATLAB Optimization Toolbox for solving nonlinear multivariate functions. The goal is to ensure that the Rq, ε, and λ of the simulated rough surface match the characteristic parameters of the real rough surface.

[0055] The comparison of autocorrelation characteristic parameters between real rough surfaces and simulated rough surfaces is shown in the table below:

[0056]

[0057] In this invention, the simulated rough surface has the same Rq as the real rough surface, while ε and λ are approximate after calculation due to human error during ranging. Therefore, the autocorrelation characteristic parameters of the simulated rough surface generated by this invention are consistent with those of the real rough surface.

[0058] As attached Figure 6 As shown, this is the autocorrelation image obtained from autocorrelation function analysis of a simulated rough surface.

[0059] Step 5: After obtaining the simulated rough surface, map it onto the interior of the air film pores.

[0060] In step 2, the coordinates of the wall convexity and concavity of the real rough surface and the simulated rough surface were obtained. In this invention, these two sets of data each have 101 data points in the x and z directions, and each x and z corresponds to a convex height y. First, the rough surface is interpolated onto a cylindrical surface perpendicular to the x-axis. Then, the coordinate points are rotated by a certain angle around the center of the cylinder's base and the cylinder's central axis to obtain the wall coordinates of the film air hole corresponding to the tilt angle calculated in this invention. To directly import the data into UG, the coordinates of the center point where the initial film air hole intersects with the cold flow are first measured in UG. Then, the coordinates of the center of the cylinder's base after rotation are obtained through trigonometric transformation. Based on these coordinate points and the previous data points, the rough surface can be interpolated into the film air hole, and the corresponding data can be exported. To facilitate subsequent modeling operations, when exporting points, every 101 data points are output sequentially, for a total of 101 files.

[0061] After exporting the data, use the spline command in NX software to import point coordinates and obtain a spline curve. Import a total of 101 point files, resulting in 101 spline curves, as shown in the attached image. Figure 7 As shown.

[0062] By connecting these 101 spline curves using the "Surface - Curve Group" operation command in NX software, the air film pores corresponding to the rough surface can be obtained, as shown in the attached figure. Figure 8As shown. Then, based on the original film cooling model, the main and secondary flow domains are completed to obtain the numerical simulation calculation domain of the film pores corresponding to the real rough surface / simulated rough surface, and then numerical simulation calculation is performed.

[0063] The calculation results are shown in the attached figure. Figure 9 The numerical verification of the film cooling efficiency distribution cloud diagrams for real and simulated rough film air flow heat transfer characteristics are shown in the attached figure. Figure 10 The lateral average cooling efficiency distribution diagram shown is attached. Figure 11 The cooling efficiency distribution along the centerline is shown in the diagram. It can be seen that the cooling efficiency of the real rough film pores and the simulated rough film pores is basically the same, except for a slight difference at the pore outlet; this indicates that the method of constructing a simulated rough surface based on the characteristic parameters obtained from the autocorrelation function is feasible.

Claims

1. A method for characterizing the roughness inside a pore and modeling a film pore based on an autocorrelation function, characterized in that... The specific steps are as follows: Step 1: Perform CT scanning on the air film pores obtained by additive manufacturing to obtain the coordinates of the actual rough air film pore surface. Represent the air film pore surface coordinates within a square through coordinate transformation and interpolation. Use the autocorrelation function to obtain the corresponding three autocorrelation characteristic parameters:

1. Height of the central peak. R AC (0,0) is numerically equal to the root mean square height of the roughness. Rq 2. The distance between the two protrusions λ, 3. The aspect ratio of the central peak protrusion, i.e., the average eccentricity of the rough element. ε ; Step 2: Use an ellipsoidal rough structure to simulate a complex rough surface, thus obtaining a simulated rough surface; Step 3: Substitute the coordinates of the simulated rough surface with ellipsoids from Step 2 into the autocorrelation function used in Step 1 to obtain the three autocorrelation characteristic parameters corresponding to the simulated rough surface. Rq , ε and λ ; Step 4: ε The values ​​of are consistent with those of a real rough surface, thus obtaining simulated rough surface parameters that correspond to the real rough surface. Rq , ε and λ ;and F D and F X The value is obtained by using the fmincon function in the MATLAB Optimization Toolbox to perform a global search and optimization, thereby obtaining a value that matches the real rough surface. Rq , ε and λ A consistent simulated rough surface; Step 5: After obtaining the square simulated rough surface, map it onto the inner surface of the film air hole; first, map the simulated rough structure onto the cylindrical film air hole coordinate system through coordinate transformation and interpolation to obtain the coordinate point cloud data of the inner surface of the film air hole; divide the point cloud data into several groups according to the direction perpendicular to the inner axis of the hole, import each group of point clouds into NX software, and form spline curves respectively; finally, establish a cylindrical surface with an ellipsoidal simulated rough morphology in NX software through several spline curves, and this cylindrical surface is the established simulated rough film air hole inner surface; In step 1, the autocorrelation function takes the form of: ； ； In the formula, x and z are the two coordinate axes of the plane, and Y(x,z) represents the surface roughness height at the (x,z) coordinate. The value represents the average of all surface roughness heights, Δx and Δz represent the coordinate differences between points on the plane, and the sign function is used. sign The peaks and valleys on the surface were distinguished; In step 2, firstly, hemispherical protrusions of different diameters are randomly generated on the surface. Then, the following formula can be used to transform the hemispherical protrusions into an ellipsoidal distribution: ； ； ； ； in, D i The diameters of randomly generated hemispheres of different diameters. ε The eccentricity of the random coarse element. F D This is the diameter scaling factor. F X Let x be the scaling factor in the x-direction; for any set of ε , F D and F X Any value of can produce a simulated rough surface with ellipsoidal protrusions.

Images