Turbine surface random roughness generation and detection method based on Gaussian noise

Abstract

The invention provides a turbine surface random roughness generation and detection method based on Gaussian noise. The turbine surface random roughness generation and detection method comprises the following steps: firstly, establishing a turbine sheet body structure node set to be added with random roughness, and determining a normal vector of each surface sheet where each node is located; secondly, generating a height according to the turbine surface roughness, and obtaining a variance and a mean value of Gaussian noise waves; controlling the node to move along the displacement direction according to a Gaussian noise function and obtaining a node displacement amount; calculating the surface roughness statistical magnitude of the turbine sheet body structure passing through the Gaussian noise, and calculating the correction coefficient of the Gaussian noise standard deviation; and finally, re-controlling the node to move along the displacement direction by utilizing the correction coefficient to obtain the turbine sheet body structure with the rough surface. According to the method, the position of the surface node after re-topology is adjusted through the Gaussian function, the displacement height and the surface normal vector, the turbine random rough surface can be efficiently and controllably generated, and research related to refined gas-heat performance analysis and evaluation of turbomachinery with the rough surface can be conveniently carried out.

Description

Technical Field

[0001] The present invention relates to the field of refined thermal analysis and performance evaluation of turbomachinery, and specifically to a method for generating and detecting random roughness on the surface of a turbine based on Gaussian noise. Background Technique

[0002] Due to the inevitable surface damage of an aero-engine turbine during manufacturing and use, the actual gas thermal performance of the turbine often deviates significantly from the designed conditions. Taking the surface roughness of the turbine as an example, spraying thermal barrier coatings during the manufacturing process and the deposition of inhaled particulate matter during operation will both cause an increase in the surface roughness of the turbine. The surface roughness on the outer surface and inside the holes of the turbine will seriously weaken the film cooling and enhance the convective heat transfer outside the turbine, bringing a greater thermal load to the turbine and threatening the safe use of the turbine. Therefore, how to carry out research on the cooling performance of the turbine under surface roughness has become the primary problem in refined turbine design and cooling margin analysis, and it is an indispensable part of turbine cooling design.

[0003] Adding roughness elements to the surface of the turbine is a prerequisite for studying the gas thermal performance of the turbine with surface roughness. Currently, mainly regular roughness elements or manual arrangement methods are used. In the literature "Surface roughness effects on external heattransfer of a hp turbine vane" (Journal of Turbomachinery, 2005, Vol. 127, No. 1, pp. 200-208), the author modeled the surface roughness of the turbine by adding regular frustums on the surface. The advantage of this method is that the size and spacing of the roughness elements can be manually controlled. However, when the magnification ratio is small, this method has high requirements for processing accuracy, and the effectiveness of this method in equivalent actual random roughness has also been widely questioned. In the literature "Effects of arealistically rough surface on vane heat transfer including the influence ofturbulence condition and Reynolds number" (Journal of Turbomachinery, 2012, Vol. 134, Article No. 021013), the author generated a rough surface through the manual arrangement method of attaching sandpaper. This method cannot accurately control the size of the roughness, and the roughness completely depends on the experience of the processing personnel, and the research results are difficult to reproduce. Summary of the Invention

[0004] Aiming at the problems that only regular roughness elements can be arranged on the turbine surface at present and it is difficult to control the artificial arrangement of random roughness, etc., the present invention proposes a method for generating and detecting random roughness on the turbine surface based on Gaussian noise. By adjusting the positions of the surface nodes after re-topology through Gaussian functions, displacement heights, and surface normal vectors, a random rough surface of the turbine can be generated efficiently and controllably, and the statistical parameters of the generated random rough surface are recalculated to complete the detection of the generated surface, so as to facilitate the development of relevant research on the refined gas thermal performance analysis and evaluation of turbomachinery with surface roughness.

[0005] The technical solution of the present invention is as follows:

[0006] The method for generating and detecting random roughness on the turbine surface based on Gaussian noise includes the following steps:

[0007] Step 1: Establish a set of node structures of the turbine blade to which random roughness is to be added, and determine the normal vectors of each patch where each node is located;

[0008] Step 2: According to the set height of turbine surface roughness, and in accordance with the 3σ principle of the normal distribution, the variance and mean of the Gaussian noise are obtained as:

[0009] μ = 0, σ = h / 3, X ∼ N(0, h 2 / 9)

[0010] where μ is the variance of the Gaussian noise, σ is the standard deviation of the Gaussian noise, h is the set roughness generation height, and X is the generated Gaussian noise function;

[0011] Step 3: According to the Gaussian noise function obtained in Step 2, control the nodes in Step 1 to move along the displacement direction, and obtain the node displacement amount Δh i , where Δh i represents the displacement amount of the i-th node; the displacement direction is the resultant vector of the normal vectors of each patch where the node is located;

[0012] Step 4: According to the displacement amounts of each node obtained in Step 3, calculate the surface roughness statistics of the turbine blade structure after Gaussian noise, including:

[0013] Arithmetic mean roughness Ra: where I is the number of nodes;

[0014] Root mean square deviation of the profile Rq:

[0015] Maximum profile peak height Rp: Rp = Max(Δh i );

[0016] Maximum profile valley depth Rv: Rv = |Min(Δh i )|;

[0017] Maximum profile height Rz: Rz = Rp + Rv;

[0018] Step 5: Based on the surface roughness statistical quantity of the turbine blade structure obtained in Step 4 and the set generation height of the turbine surface roughness, according to the formula

[0019] α = 2·h / Rz

[0020] calculate the correction coefficient α of the standard deviation of Gaussian noise;

[0021] Step 6: Use the correction coefficient α of the standard deviation of Gaussian noise obtained in Step 5 to re-control the nodes in Step 1 to move along the displacement direction, and obtain a surface-rough turbine blade structure that is exactly the same as the set generation height of the turbine surface roughness.

[0022] Further, the specific process of Step 1 is as follows:

[0023] Step 1.1: In 3D software, establish a turbine blade model to which random roughness is to be added;

[0024] Step 1.2: Determine the number of topological patches, and re-topologize the turbine blade model using triangular patches to obtain a finely divided turbine blade structure;

[0025] Step 1.3: In the finely divided turbine blade structure obtained in Step 1.2, determine the position of each node of the triangular patch and the normal vector of each patch where each node is located.

[0026] Further, in Step 3, the expression for the node to move along the displacement direction is:

[0027]

[0028] where n i (x 0 , y 0 , z 0 ) represents the initial coordinates of the i-th node as (x 0 , y 0 , z 0 ), and n i (x, y, z) represents the coordinates of the i-th node after movement as (x, y, z), is the resultant vector of the unit normal vectors of each patch where the node is located, and N(0,1) is the standard normal distribution.

[0029] Further, in Step 3, Δh i = [σ·N(0,1) + μ] i .

[0030] Further, in step 6, the expression for controlling the movement of the node along the displacement direction by using the correction coefficient α is:

[0031]

[0032] Beneficial effects

[0033] A method for generating and detecting random roughness on the surface of a turbine based on Gaussian noise proposed by the present invention has the following advantages:

[0034] 1. By re-topologizing the turbine blade body and adding Gaussian noise according to the research scope of the actual roughness of the turbine, the difficulty of generating random roughness is greatly reduced. It can replace the traditional equivalent method of regular rough elements and is more in line with engineering practice.

[0035] 2. The standard deviation and mean of the corresponding Gaussian noise can be designed according to the research scope of the actual roughness of the turbine. The surface rough turbine blade body structure can be generated through a controllable normal distribution function, which can avoid the uncontrollability and difficulty of repetition in generating a rough surface by the manual layout method.

[0036] 3. After the rough surface is generated, the corresponding statistical parameters can be calculated. By adding a correction coefficient of the standard deviation of Gaussian noise to the node displacement amount, a surface rough turbine blade body structure exactly the same as the set roughness generation height can be obtained.

[0037] The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Description of the drawings

[0038] The above and / or additional aspects and advantages of the present invention will become obvious and easy to understand from the description of the embodiments in conjunction with the following drawings, where:

[0039] Figure 1 is the STL geometric model of the original film hole in the embodiment of the present invention;

[0040] Figure 2 is the STL geometric model of the re-topologized film hole in the embodiment of the present invention;

[0041] Figure 3 is the STL geometric model of the film hole with added noise in the embodiment of the present invention;

[0042] Figure 4 is the coordinate point displacement amount and statistical parameters of the film hole in the embodiment of the present invention;

[0043] Figure 5 is the circumferential shape of the intersection line of the flow direction cross-section of the film hole in the embodiment of the present invention;

[0044] Figure 6 The computational domain of flat-film cooling with random roughness inside the holes in the embodiments of the present invention;

[0045] Figure 7 The flat-film cooling effectiveness distribution of the flat-film with random roughness inside the holes in the embodiments of the present invention;

[0046] Figure 8 The spanwise-averaged flat-film cooling effectiveness of the flat-film with random roughness inside the holes in the embodiments of the present invention. Detailed implementation manners

[0047] The embodiments of the present invention will be described in detail below. The embodiments are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0048] The method for generating and detecting random roughness on the turbine surface based on Gaussian noise in this embodiment includes the following steps:

[0049] Step 1: Establish a set of node structures of the turbine blade body to which random roughness is to be added, and determine the normal vectors of each surface patch where each node is located; specifically, it includes the following steps:

[0050] Step 1.1: In 3D software, establish a turbine blade body model to which random roughness is to be added; as Figure 1 shown, adopt the STL geometric file format to establish the turbine film hole blade body structure to which random roughness is to be added;

[0051] Step 1.2: Determine the number of topological surface patches according to the structural complexity and the set height of roughness generation and the rough element spacing, and re-topologize the turbine blade body model with triangular surface patches to obtain a finely divided turbine film hole blade body structure;

[0052] The re-topologized STL blade body file contains the node positions and surface normal vector information of the triangular surface patches. Therefore, in the finely divided turbine blade body structure obtained in step 1.2, determine the position of each node of the triangular surface patch and the normal vectors of each surface patch where each node is located.

[0053] Step 2: According to the set height of the film hole roughness on the turbine surface, and in accordance with the 3σ principle of the normal distribution, obtain the variance and mean of the Gaussian noise as:

[0054] μ = 0, σ = h / 3, X ~ N(0, h 2 / 9)

[0055] where μ is the variance of the Gaussian noise, σ is the standard deviation of the Gaussian noise, h is the set height for generating roughness, and X is the generated Gaussian noise function; in this embodiment, the diameter of the film hole is 4 mm, the set height for generating the roughness of the film hole is 0.32 mm, the mean of the normal distribution is 0, the standard deviation of the normal distribution is 0.1067, and the normal distribution is X ~ N(0, 0.01138).

[0056] Step 3: According to the Gaussian noise function obtained in Step 2, control the nodes in Step 1 to move along the resultant vector of the unit normal vectors of each patch where they are located, and obtain a surface-rough film hole structure with Gaussian noise characteristics as Figure 3 shown, where the expression for the node movement is:

[0057]

[0058] where n i (x 0 , y 0 , z 0 ) represents the initial coordinates of the i-th node as (x 0 , y 0 , z 0 ), and n i (x, y, z) represents the coordinates of the i-th node after movement as (x, y, z), is the resultant vector of the unit normal vectors of each patch where the node is located, and N(0, 1) is the standard normal distribution;

[0059] And extract the noise information in the STL file for the surface-rough film hole sheet structure to obtain the node displacement Δh i :

[0060] Δh i = [σ·N(0, 1) + μ] i

[0061] where Δh i represents the displacement of the i-th node.

[0062] Step 4: According to the displacement of each node obtained in Step 3, calculate the surface roughness statistics of the turbine sheet structure after surface roughness is achieved through Gaussian noise processing, including:

[0063] Arithmetic mean roughness Ra: where I is the number of nodes; in this embodiment, the arithmetic mean roughness of the surface-rough film hole sheet is 0.064 mm;

[0064] Root mean square deviation of the profile Rq: In this embodiment, the root mean square deviation of the profile of the surface-rough film hole sheet is 0.080 mm;

[0065] Maximum profile peak height Rp: Rp = Max(Δh i ); In this embodiment, the maximum profile peak height of the surface-roughened film hole sheet body is 0.289 mm;

[0066] Maximum profile valley depth Rv: Rv = |Min(Δh i )|; In this embodiment, the maximum profile valley depth of the surface-roughened film hole sheet body is 0.291 mm;

[0067] Profile maximum height Rz: Rz = Rp + Rv; In this embodiment, the profile maximum height of the surface-roughened film hole sheet body is 0.580 mm.

[0068] Step 5: According to the surface roughness statistics of the turbine blade body structure obtained in Step 4 and the set turbine surface roughness generation height, according to the formula

[0069] α = 2·h / Rz

[0070] Calculate the correction coefficient α of the Gaussian noise standard deviation; In this embodiment, the correction coefficient of the Gaussian noise standard deviation is 1.0934.

[0071] Step 6: Use the correction coefficient α of the Gaussian noise standard deviation obtained in Step 5 to re-control the movement of the nodes in Step 1 along the resultant vector of the unit normal vectors of each patch, and obtain a surface-roughened turbine blade body structure that is exactly the same as the set turbine surface roughness generation height. The expression for controlling the node movement using the correction coefficient α is:

[0072]

[0073] As Figure 4 and Figure 5 , in this embodiment, a surface randomly roughened film hole sheet body with a maximum rough height of 0.32 mm is obtained through the above generation and detection.

[0074] Simulation example:

[0075] Perform 3D modeling on the surface randomly roughened film hole sheet body obtained in Step 6 to obtain a flat plate film cooling calculation domain with random roughness inside the holes; Perform mesh division and 3D simulation calculation on the flat plate film cooling calculation domain, and the specific flat plate film cooling efficiency distribution affected by the roughness inside the holes is as follows:

[0076] Divide the calculation domain using tetrahedral elements, and complete the independence verification of the mesh division and the setting of relevant calculation conditions, where: The turbulence model selects the SST γ-θ model, the mainstream uses a velocity inlet and a pressure outlet, the cold air uses a mass flow inlet, and the blowing ratio of the cold air is 1.0;

[0077] As Figure 7 and Figure 8, the film cooling holes with randomly rough surfaces obtained by the present invention are compared with the smooth holes in terms of film cooling effectiveness and spanwise-averaged film cooling effectiveness. After the inner surfaces of the holes are roughened, the spanwise coverage of the film cooling at various downstream positions is significantly reduced, and the spanwise-averaged film cooling effectiveness is significantly lower than that of the smooth holes.

[0078] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for generating and detecting random roughness of turbine surface based on Gaussian noise, characterized in that: The following steps are involved: Step 1: Establish a set of turbine blade structure nodes to be added with random roughness, and determine the normal vectors of each facet where each node is located; Step 2: Generate the height according to the set turbine surface roughness. According to the 3σ principle of normal distribution, the variance and mean of Gaussian noise are: μ=0,σ=h / 3,X~N(0,h 2 / 9) Where μ is the variance of Gaussian noise, σ is the standard deviation of Gaussian noise, h is the set roughness generation height, and X is the generated Gaussian noise function; Step 3: According to the Gaussian noise function obtained in step 2, control the node in step 1 to move along the displacement direction, and obtain the node displacement Δh i , where Δh i represents the displacement of the ith node; the displacement direction is the sum of the normal vectors of each facet where the node is located; Step 4: According to the displacement of each node obtained in step 3, the surface roughness statistics of the turbine blade structure after Gaussian noise are calculated, including: Arithmetic mean roughness Ra: Where I is the number of nodes; Profile root mean square deviation Rq: Maximum profile peak height Rp: Rp = Max(Δh i ); Maximum valley depth Rv: Rv = |Min(Δh i )|; Maximum profile height Rz: Rz = Rp + Rv; Step 5: Based on the surface roughness statistics of the turbine body structure obtained in step 4 and the set turbine surface roughness generation height, according to the formula α=2·h / Rz Calculate the correction coefficient α of the Gaussian noise standard deviation; Step 6: Use the correction coefficient α of the Gaussian noise standard deviation obtained in step 5 to re-control the movement of the nodes in step 1 along the displacement direction to obtain a surface roughened turbine sheet structure having the same height as the set turbine surface roughness generation height.

2. The method for generating and detecting random roughness of turbine surface based on Gaussian noise according to claim 1, characterized in that: The specific process of step 1 is: Step 1.1: In the 3D software, establish a turbine blade model to which random roughness is to be added; Step 1.2: Determine the number of topological facets, and use triangular facets to retopologize the turbine blade model to obtain a finely divided turbine blade structure; Step 1.3: In the finely divided turbine blade structure obtained in step 1.2, determine the position of each node of the triangular face and the normal vector of each face where each node is located.

3. The method for generating and detecting random roughness of turbine surface based on Gaussian noise according to claim 1, characterized in that: In step 3, the expression for the movement of the node along the displacement direction is: where n i (x0, y0, z0) means the initial coordinates of the i-th node are (x0, y0, z0), n i (x,y,z) means the coordinates of the i-th node after moving are (x,y,z). is the sum of the unit normal vectors of each face where the node is located, and N(0,1) is the standard normal distribution.

4. The method for generating and detecting random roughness of turbine surface based on Gaussian noise according to claim 3 is characterized in that: In step 3, Δh i =[σ·N(0,1)+μ] i .

5. The method for generating and detecting random roughness of turbine surface based on Gaussian noise according to claim 3, characterized in that: In step 6, the expression for controlling the movement of the node along the displacement direction using the correction coefficient α is:

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