A geometric uncertainty modeling method for compressor blade fouling

Abstract

This invention relates to the field of compressor blade fouling, and particularly to a two-dimensional geometric uncertainty modeling method for compressor blade fouling. Based on the actual morphology of compressor blade fouling, the fouling is divided into a compact layer and a loose layer along the blade profile normal. Considering the uncertainty of fouling distribution on the compressor blade surface under actual operating conditions, a sparse compact layer fouling geometric uncertainty model is constructed by combining the KL expansion method with a sparse grid numerical integration method, and a randomized coarse loose layer fouling geometric uncertainty model is also established. The geometric uncertainty modeling method for compressor blade fouling provided by this invention is applicable to establishing geometric uncertainty models for compressor blades with arbitrary fouling distributions. The sparse blade fouling geometric model represents all geometric models within the entire distribution space, making it particularly suitable for providing CFD calculation geometric models for predicting the probability of aerodynamic performance degradation in fouled compressor blades.

Description

Technical Field

[0001] This invention relates to the field of compressor blade fouling modeling, and particularly to a two-dimensional geometric uncertainty modeling method for compressor blade fouling. Technical Background

[0002] During frequent changes in flight conditions (takeoff, climb, cruise, afterburner, low altitude, landing, etc.), suspended particulate matter in the atmosphere (dust, soot, hydrocarbon aerosols, pollen, and salt, etc.) is inevitably drawn into the aircraft engine. Some of this particulate matter deposits and accumulates over a long period, forming fouling on the compressor blade surface. Compressor blades are small in size and operate under high loads, making their performance extremely sensitive to blade profiles. Fouling not only alters the compressor blade geometry, increasing flow losses, but also clogs flow channels, reducing the engine's flow capacity.

[0003] Blade surface fouling exhibits diversity under the combined influence of multiple factors, including atmospheric environment, deposition time, operating conditions, and blade geometry. However, blade fouling formed within a certain operating time inevitably displays randomness (i.e., uncertainty) on a macroscopic level, conforming to a certain statistical distribution law, and exhibits multi-scale roughness characteristics on a microscopic level. Therefore, establishing a geometric uncertainty model for compressor blade fouling that considers the uncertainty of fouling distribution is beneficial for predicting the probability of compressor aerodynamic performance degradation due to the uncertainty of fouling distribution.

[0004] Common uncertainty analysis methods include sampling methods, local expansion methods, and numerical integration methods. Sampling methods offer higher accuracy compared to other methods, but require a large number of samples, resulting in a very high computational cost. Local expansion methods are often used for estimating failure probabilities. Numerical integration methods are a relatively new uncertainty analysis approach, derived from Gaussian quadrature formulas. They offer high algebraic accuracy, but the number of samples required increases exponentially with the dimensionality of the independent variable. However, geometric modeling of compressor blade fouling is a complex high-dimensional problem, facing the curse of dimensionality in uncertainty modeling.

[0005] Current methods for modeling compressor blade fouling primarily rely on uniform thickness and equivalent gravel models, and are all deterministic studies. However, real blade fouling exhibits uncertain, non-uniform thickness and random roughness, making compressor aerodynamic performance extremely sensitive to blade profiles. Therefore, developing efficient geometric uncertainty modeling methods for compressor blade fouling, fully considering the non-uniform thickness distribution and rough microstructure of the fouling, is the foundation and prerequisite for further achieving "pre-prediction" of aerodynamic performance degradation in fouled compressors. Summary of the Invention

[0006] The purpose of this invention is to consider the uncertainty of fouling distribution and use a sparse compressor fouling blade geometric model to represent all geometric uncertainty models in the entire distribution space, thereby providing a CFD calculation model for predicting the probability of aerodynamic performance degradation of fouling compressor blades.

[0007] To achieve the above objectives, this invention provides a geometric modeling method for compressor blade fouling with uncertain fouling distribution, comprising the following steps:

[0008] Step 1: Based on the morphological characteristics of the blade fouling, the blade fouling is divided into two parts, a dense layer and a loose layer, in the normal direction of the blade profile. In the tangential direction, both the dense layer fouling and the loose layer fouling are defined as functions that vary along the length of the blade profile line, denoted as h1(s) and h2(s) respectively, where s represents the length coordinate of the blade profile line, and the fouling size is defined as y = h1(s) + h2(s).

[0009] Step 2: Calculate the total length of the clean leaf profile and normalize the length of the clean leaf profile, i.e., s∈[0,1];

[0010] Step 3, establishing an uncertainty model for densely deposited fouling, specifically includes:

[0011] Step 3.1: Construct parametric control points for the airfoil based on its geometric profile. The trailing edge point is designated as the first control point. All control points on the airfoil are then arranged in the order of trailing edge point, suction surface control point, leading edge point, pressure surface control point, and back to trailing edge point. The normalized coordinate values ​​of the control points are calculated and used as the independent variable in the calculation of the compacted fouling function. The number of control points is denoted as N, i.e., h1(s1,s2,s3,…,s…). i ,…s N );

[0012] Step 3.2: Determine the control parameters for the scale distribution at the control points, and construct the covariance matrix C of the dense scale layer at the control points. cov Defined as:

[0013]

[0014] Where, σ(s) i ) represents the control parameter for the distribution of densely deposited scale at the control point, ρ(s) i ,s j The correlation between adjacent control points is represented by (), specifically defined as:

[0015]

[0016] Where L represents the correlation length between the two control points, defined as:

[0017]

[0018] Specifically, Defined as:

[0019]

[0020] Where r is the leading edge radius of the clean airfoil, L0 is usually taken as 10 times the leading edge radius, L LE It is one-quarter of the leading edge radius.

[0021] Step 3.3, calculate the covariance matrix C cov Based on the eigenvalues ​​and eigenvectors, the scale size at the control point location of the compact scale is calculated using the KL expansion method. The compact scale distribution is transformed into a standard Gaussian distribution space. The calculation formula of the KL expansion method is defined as follows:

[0022]

[0023] Where θ represents the random space of densely deposited fouling, λ i Let C be the covariance matrix. cov The i-th eigenvalue, Let C be the covariance matrix. cov The eigenvector corresponding to the i-th eigenvalue, ζ i (Ω) represents independent and identically distributed random variables that satisfy a standard Gaussian distribution. M represents the number of eigenvalues ​​and eigenvectors required to construct the contour coordinates of tightly deposited fouling. The eigenvectors of the covariance matrix are arranged from largest to smallest. An appropriate cutoff percentage k is selected according to the convergence condition to determine the number of eigenvalues ​​required to calculate the contour coordinates of tightly deposited fouling. The formula for calculating M is defined as follows:

[0024]

[0025] Step 3.4: Based on the calculation results in Step 3.2, the dimension of the function independent variable of the compact layered fouling is reduced from N to M. A sparse numerical grid integration algorithm with M-dimensional variables is constructed to solve for the integration nodes and weights of the M-dimensional compact layered fouling. The integration nodes are the independent and identically distributed random variables ζ satisfying the standard Gaussian distribution obtained in Step 3.3. i (Ω), the integration nodes N of the specific sparse grid numerical integration algorithm t-SG and corresponding weights ω SG Defined as:

[0026]

[0027] Where k is the horizontal precision of the sparse grid (k≥0), the larger the value of k, the higher the precision. The multi-exponential combination is defined as |I|=I1+I2+…I M And it is limited to a certain interval, with specific integration nodes. and corresponding weights Calculated based on the numerical integral formula corresponding to the distribution of densely deposited scale.

[0028] Step 3.5: Substitute the calculation results from steps 3.3 and 3.4 into the definition of the KL expansion method to solve for the scale size h1 at the location of the compact scale blade control point.

[0029] Step 4, establishing an uncertainty model for loose deposits, specifically including:

[0030] Step 4.1: To accurately describe the multi-scale roughness characteristics of blade fouling while meeting mesh generation requirements, interpolation is performed on the blade profile length coordinates from Step 2, ensuring l1μm ≤ Δs. i ≤l2μm, where Δs i =s i+1 -s i The multi-scale rough morphology of loosely deposited fouling is described using as many points as possible, and all coordinates are multiplied by the total length of the leaf profile to obtain the modeling independent variables of loosely deposited fouling.

[0031] Step 4.2: Construct a loose stratification fouling roughness model based on the improved Longuet-Higgins wave model, denoted as the Longuet-Higgins-fouling (LHF) fouling model. Use the x-coordinate of the interpolated blade profile length from Step 4.1 as the independent variable of the LHF fouling model, and give the amplitude 'a' of the loose stratification fouling wave crest. n , using ω n Controlling the roughness frequency of loose deposits, K n Controlling the wave number of individual component waves in the rough profile of loosely deposited scale. The skew angle of the component waves that control the rough profile of loosely deposited scale, ε n To ensure the randomness of the initial phase of the rough profile of the loose fouling layer and to conform to a uniformly distributed random number, different roughness frequencies, degrees of skewness, and roughness sizes can be established by adjusting various control parameters. The LHF fouling model is defined as follows:

[0032]

[0033] Wherein, the loose layer of fouling calculated by the LHF fouling model is positive, defined as:

[0034]

[0035] Roughness frequency control parameter ω of loose deposited scale profile n Defined as:

[0036] ω n=c∈

[0037] Where ∈ is a d-dimensional column vector that follows a standard Gaussian distribution, and c is a constant;

[0038] K n With ω n Related, defined as:

[0039]

[0040] In this example, the control parameters for the skew direction angle of the component waves of the rough profile of loosely deposited fouling are... Defined as:

[0041]

[0042] Where η is a d-dimensional column vector that follows a standard Gaussian distribution;

[0043] Where, ε n Let be a uniformly distributed set of d-dimensional column vectors, and obey ε. n ~U(a, b);

[0044] Step 5: Normalize the abscissa of the loose deposits calculated in Step 4.1, and interpolate the distribution of all the tight deposits established in Step 3 along different control points to obtain the distribution of all the tight deposits along the blade profile coordinates. Calculate the size of the deposit distribution along the blade profile, y = h1(s) + h2(s), to obtain the blade profile coordinates of the deposits at the corresponding position of the blade profile.

[0045] Step 6, Step 6 is the calculation of the coordinate points of the scale buildup blade, specifically including:

[0046] Step 6.1: Along the coordinate direction of the blade profile arc, based on the coordinates calculated in Step 4.1, select two closest coordinate points A and B on the clean blade profile to form a vector. Calculate vectors The angle θ between the axial direction and the chord length direction;

[0047] Step 6.2: Based on the obtained size y of the dirt accumulation at coordinate point A and the included angle θ, calculate the vector... Perpendicular vectors Solving vectors The coordinate points of the scale buildup on the blade shape;

[0048] Step 6.3: Repeat steps 6.1 and 6.2 until the coordinates of the airfoil after all locations on the clean airfoil have accumulated dirt are obtained.

[0049] Step 6.4: Smoothly connect all the scale coordinates of each modeling result to obtain the outline of the scale blade shape.

[0050] Compared with existing methods, the beneficial effects of the present invention are:

[0051] (1) This invention takes into account the uncertainty characteristics of the actual compressor blade fouling distribution. The established fouling blade geometric uncertainty model has the non-uniform uncertainty and multi-scale roughness uncertainty characteristics of the actual compressor blade fouling distribution, breaking through the technical bottleneck of existing blade fouling research that relies solely on the rough wall solution algorithm of CFD solver.

[0052] (2) This invention takes into account the uncertainty characteristics of the geometric distribution of fouling on real compressor blades and is not limited by the shape of compressor blades. In the modeling stage, fewer blade fouling geometric samples are constructed to represent all samples of the fouling uncertainty distribution, which greatly reduces the number of CFD calls and can reduce the prediction time of the probability of aerodynamic performance degradation of fouling compressors.

[0053] (3) The blade fouling model established in this invention does not rely on fouling distribution data during service. It provides a sample library of fouling blade geometric models for predicting the probability of aerodynamic performance degradation of compressor blades by fouling during the design phase, and has a wider range of applicability. Attached Figure Description

[0054] Figure 1 Flowchart for modeling geometric uncertainties of blade fouling;

[0055] Figure 2 This is a schematic diagram of a scale-accumulating blade.

[0056] Figure 3 A schematic diagram showing the location of control points for densely deposited scale in a certain leaf-shaped structure;

[0057] Figure 4 This is an example of the distribution of the mean and standard deviation of the control points for dense deposits on a compressor blade.

[0058] Figure 5 To establish a map of all samples for the distribution of densely deposited fouling;

[0059] Figure 6 A schematic diagram of the distribution of loosely deposited scale in a sample.

[0060] Figure 7 This is a schematic diagram illustrating the method of depositing dirt on a clean blade.

[0061] Figure 8 Figure showing the modeling results for the geometric uncertainty of blade fouling. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0063] Step 1: Based on the morphological characteristics of the blade fouling, the blade fouling is divided into two parts, a dense layer and a loose layer, in the normal direction of the blade profile. In the tangential direction, both the dense layer fouling and the loose layer fouling are defined as functions that vary along the length of the blade profile line, denoted as h1(s) and h2(s) respectively, where s represents the length coordinate of the blade profile line, and the fouling size is defined as y = h1(s) + h2(s).

[0064] Step 2: Calculate the total length of the clean leaf profile and normalize the length of the clean leaf profile, i.e., s∈[0,1];

[0065] Step 3, establishing an uncertainty model for densely deposited fouling, specifically includes:

[0066] Step 3.1: Construct parametric control points for the airfoil based on its geometric profile. The trailing edge point is designated as the first control point. All control points on the airfoil are then arranged in the order of trailing edge point, suction surface control point, leading edge point, pressure surface control point, and back to trailing edge point. The normalized coordinate values ​​of the control points are calculated and used as the independent variable in the calculation of the compacted fouling function. The number of control points is denoted as N. In this example, the number of control points is 39, i.e., N = 39, and h1(s1, s2, s3, ..., s i , …s N );

[0067] Step 3.2: Given the control parameters for the scale distribution at the control point, in this example, the scale in the compact layer at the control point follows a Gaussian distribution, and the control parameter is the mean μ(s). i ) and standard deviation σ(s i The distribution of control points is illustrated in the attached figure. The covariance matrix C of the tightly deposited fouling at each control point is constructed. cov Defined as:

[0068]

[0069] Wherein, ρ(s) i ,s j The correlation between adjacent control points is represented by (), specifically defined as:

[0070]

[0071] Where L represents the correlation length between the two control points, defined as:

[0072]

[0073] Specifically, Defined as:

[0074]

[0075] Where r is the leading edge radius of the clean airfoil, L0 is 10 times the leading edge radius, and L LE It is one-quarter of the leading edge radius.

[0076] Step 3.3 Calculate the covariance matrix C cov Based on the eigenvalues ​​and eigenvectors, the scale of the compact scale at the control point location is calculated using the KL expansion method. This transforms the non-stationary Gaussian distributed compact scale into a standard Gaussian distributed compact scale. The calculation formula for the KL expansion method is defined as follows:

[0077]

[0078] Where θ represents the random space of densely deposited fouling, λ i Let C be the covariance matrix. cov The i-th eigenvalue, Let C be the covariance matrix. cov The eigenvector corresponding to the i-th eigenvalue, ζ i (Ω) represents independent and identically distributed random variables that satisfy a standard Gaussian distribution. M represents the number of eigenvalues ​​and eigenvectors required to construct the contour coordinates of tightly deposited fouling. The eigenvectors of the covariance matrix are arranged from largest to smallest. An appropriate truncation percentage is selected according to the convergence condition to determine the number of eigenvalues ​​required to calculate the contour coordinates of tightly deposited fouling. The formula for calculating M is defined as follows:

[0079]

[0080] In this example, k=99, that is, the contour coordinates of the dense deposit are constructed based on the first 99% of the eigenvalues ​​of the covariance matrix of the dense deposit. The calculation result in this example is M=9.

[0081] Step 3.4: Based on the calculation results of Step 3.2, the dimension of the function independent variable of the compact layered fouling is reduced from N=39 to M=9. A sparse numerical grid integration algorithm with 9-dimensional variables is constructed to solve for the integration nodes and weights of the compact layered fouling with 9-dimensional variables. The integration nodes are the independent and identically distributed random variables ζ satisfying the standard Gaussian distribution obtained in Step 3.3. i (Ω), the integration nodes N of the specific sparse grid numerical integration algorithm t-SG and corresponding weights ω SG Defined as:

[0082]

[0083] In this example, a sparse mesh with a horizontal precision of k=3 is chosen to solve for the multi-exponential combinations of 9-dimensional variables. A total of 1330 combinations are calculated, meaning that 1330 compact deposit fouling models can be constructed to characterize all 3.0223×10⁻⁶ compact deposit fouling controlled by the 39-dimensional variables in this example. 23 A tight-layered fouling geometry model (the formula for calculating Num for all tight-layered fouling geometry models is: Num = (k + 1) N ), specific Gaussian integral nodes and corresponding weights Calculated based on Gauss-Emilt numerical integration.

[0084] Step 3.5: Substitute the calculation results from steps 3.3 and 3.4 into the definition of the KL expansion method to solve for the scale size h1 at the location of the compact scale blade control point.

[0085] Step 4, establishing an uncertainty model for loose deposits, specifically including:

[0086] Step 4.1: To accurately describe the multi-scale roughness characteristics of blade fouling while meeting mesh generation requirements, the blade profile length coordinates from Step 2 are interpolated. In this example, Δs is used. i =20μm, ensuring that as many points as possible are used to describe the multi-scale rough morphology of loosely deposited fouling, and multiplying all coordinates by the total length of the leaf profile to obtain the modeling independent variables of loosely deposited fouling;

[0087] Step 4.2: Based on the optimized Longuet-Higgins wave model, a loose stratification roughness model is constructed, denoted as the Longuet-Higgins-fouling (LHF) fouling model. The x-coordinate of the interpolated blade profile length from Step 4.1 is used as the independent variable of the LHF fouling model, given the amplitude 'a' of the loose stratification wave crest. n , using ω n Controlling the roughness frequency of loose deposits, K n Controlling the wave number of individual component waves in the rough profile of loosely deposited scale. The skew angle of the component waves that control the rough profile of loosely deposited scale, ε n To ensure the randomness of the initial phase of the rough profile of loosely deposited scale and to conform to a uniformly distributed random number, the LHF scale model is defined as follows:

[0088]

[0089] Wherein, the loose layer of fouling calculated by the LHF fouling model is positive, defined as:

[0090]

[0091] In this example, we select d = 100, an = 0.1, and ω as the roughness frequency control parameter for the loose deposit profile. n Defined as:

[0092] ω n =c∈

[0093] in, ∈ The vector is a 100-dimensional column vector that follows a standard Gaussian distribution, where c is a constant, and in this example c = 5;

[0094] K n With ω n Related, defined as:

[0095]

[0096] In this example, the control parameters for the skew direction angle of the component waves of the rough profile of loosely deposited fouling are... Defined as:

[0097]

[0098] Where η is a 100-dimensional column vector that follows a standard Gaussian distribution. In this example, based on the number of compacted fouling models, the number of loose fouling models is determined to be 1330. With other parameters remaining unchanged, 1330 sets of 100-dimensional column vectors are randomly generated to construct loose fouling geometric models with different rough profile skew directions.

[0099] In this example, ε n A uniformly distributed set of 100-dimensional column vectors that obey ε n ~U(0,5);

[0100] Step 5: Normalize the abscissa of the loose deposits calculated in Step 4.1, and interpolate the distribution of all the tight deposits established in Step 3 along different control points to obtain the distribution of all the tight deposits along the blade profile coordinates. Calculate the size of the deposit distribution along the blade profile, y = h1(s) + h2(s), to obtain the blade profile coordinates of the deposits at the corresponding position of the blade profile.

[0101] Step 6, Step 6 is the calculation of the coordinate points of the scale buildup blade, specifically including:

[0102] Step 6.1: Along the coordinate direction of the blade profile arc, based on the coordinates calculated in Step 4.1, select two closest coordinate points A and B on the clean blade profile to form a vector. Calculate vectors The angle θ between the axial direction and the chord length direction;

[0103] Step 6.2: Based on the obtained size y of the dirt accumulation at coordinate point A and the included angle θ, calculate the vector... Perpendicular vectors Solving vectors The coordinate points of the scale buildup on the blade shape;

[0104] Step 6.3: Repeat steps 6.1 and 6.2 until the coordinates of the airfoil after all locations on the clean airfoil have accumulated dirt are obtained.

[0105] Step 6.4: Smoothly connect all the fouling coordinates of each modeling result to obtain the profile of the fouling blade.

[0106] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for modeling the geometric uncertainty of compressor blade fouling, characterized in that: Includes the following steps: Step 1: Based on the morphological characteristics of blade fouling, the blade fouling is divided into two parts: a dense layer and a loose layer in the normal direction of the blade profile. In the tangential direction, both the dense and loose layers of fouling are defined as functions varying along the blade profile line, denoted as follows: h 1( s )and h 2( s ), s Represents the coordinates of the blade profile arc length and defines the size of the buildup. y = h 1( s )+ h 2( s ); Step 2: Calculate the total length of the clean airfoil profile and normalize the length of the clean airfoil profile arc. ; Step 3, establishing an uncertainty model for densely deposited fouling, specifically includes: Step 3.1: Construct parametric control points for the airfoil based on its geometric profile. The trailing edge point is designated as the first control point. Arrange the coordinates of all control points on the airfoil in the order of trailing edge point, suction surface control point, leading edge point, pressure surface control point, and back to trailing edge point. Calculate the normalized coordinate values ​​of the control points, which will be used as the independent variable in the calculation of the compacted fouling function. The number of control points is denoted as... N ,Right now ; Step 3.2: Determine the control parameters for the distribution of densely deposited scale at the control points, and construct the covariance matrix of the densely deposited scale at the control points. C cov Defined as: Where, σ( s i ) represents the control parameter for the distribution of densely deposited scale at control points. The correlation between adjacent control points is specifically defined as: in, L The correlation length between two control points is defined as: Specifically, Defined as: in, r The leading edge radius of a clean leaf shape. L 0 is taken as 10 times the leading edge radius. L LE It is one-quarter of the leading edge radius; Step 3.3, Calculate the covariance matrix C cov Based on the eigenvalues ​​and eigenvectors, the fouling size at the control points of the compact fouling layer is calculated using the KL expansion method. The compact fouling distribution is transformed into a standard Gaussian distribution space. The calculation formula of the KL expansion method is defined as follows: in, θ The random space representing tightly packed deposits. Covariance matrix C cov The i 1 eigenvalue, Covariance matrix C cov The i The eigenvectors corresponding to each eigenvalue. Let them be independent and identically distributed random variables that satisfy a standard Gaussian distribution. M To determine the number of eigenvalues ​​and eigenvectors needed to construct the contour coordinates of tightly deposited fouling, the eigenvectors of the covariance matrix are arranged from largest to smallest, and a truncation percentage is selected based on convergence. k Determine the number of eigenvalues ​​required for calculating the contour coordinates of tightly deposited scale. M The calculation formula is defined as follows: Step 3.4, based on the calculation results of Step 3.2, change the dimension of the functional independent variable of the densely deposited fouling from... N Down to M , build M A sparse numerical grid integration algorithm for dimensional variables is used to solve the problem. M The integral nodes and weights of the tightly stacked variables are given, where the integral nodes are the independent and identically distributed random variables satisfying the standard Gaussian distribution obtained in step 3.

3. The integration nodes of the specific sparse grid numerical integration algorithm N t-SG and corresponding weights Defined as: in, k For the horizontal accuracy of the sparse grid, where , k The larger the value, the higher the precision. Multiple exponent combinations are defined as follows: And it is limited to a certain interval, with specific integration nodes. and corresponding weights Calculated based on the numerical integral quadrature formula corresponding to the distribution of densely deposited fouling; Step 3.5: Substitute the calculation results from steps 3.3 and 3.4 into the definition of the KL expansion method to solve for the scale size at the location of the compacted scale blade control point. h 1; Step 4, establishing an uncertainty model for loose deposits, specifically including: Step 4.1: Interpolate the length coordinates of the leaf profile line from Step 2. ,Pick The multi-scale rough morphology of loosely deposited fouling is described using as many points as possible, and all coordinates are multiplied by the total length of the leaf profile to obtain the modeling independent variables of loosely deposited fouling. Step 4.2: Construct a loose stratification fouling roughness model based on the improved Longuet-Higgins wave model, denoted as the Longuet-Higgins-fouling (LHF) fouling model. Use the x-coordinate of the interpolated blade profile length from Step 4.1 as the independent variable of the LHF fouling model, and specify the amplitude of the loose stratification fouling wave crest. a n ,use Controlling the roughness frequency of loose deposits, K n Controlling the wave number of individual component waves in the rough profile of loosely deposited scale. Control the skew angle of the component waves that make up the rough profile of loosely deposited scale. To ensure the randomness of the initial phase of the rough profile of the loose fouling layer and to conform to a uniformly distributed random number, different roughness frequencies, degrees of skewness, and roughness sizes can be established by adjusting various control parameters. The LHF fouling model is defined as follows: in, l The loose deposits calculated by the LHF deposit model are considered positive, defined as follows: Roughness frequency control parameters for loose deposits Defined as: in, To follow a standard Gaussian distribution d A column vector of dimensionless dimensions, where c is a constant; K n and Related, defined as: Control parameters for the skew direction angle of the component waves in the rough profile of loosely deposited scale Defined as: in, To follow a standard Gaussian distribution d 3D column vector; in, A set of uniformly distributed d A column vector of dimension, satisfying... ; Step 5: Normalize the abscissa of the loose deposits calculated in Step 4.

1. Based on this, interpolate the distribution of all tightly deposited deposits along different control points established in Step 3 to obtain the distribution of all tightly deposited deposits along the blade profile coordinates. Calculate the magnitude of the deposit distribution along the blade profile. y = h 1( s )+ h 2( s ), thus obtaining the coordinates of the fouling blade profile at the corresponding position of the blade profile; Step 6, Step 6 is the calculation of the coordinate points of the scale buildup blade, specifically including: Step 6.1: Along the coordinate direction of the blade profile arc, based on the coordinates calculated in Step 4.1, select two closest coordinate points A and B on the clean blade profile to form a vector. Calculate vector Angle with the axial chord length direction θ ; Step 6.2, based on the obtained size of the scale at coordinate point A. y and included angle θ Calculation and vectors Perpendicular vectors Solve for vectors The coordinate points of the scale buildup on the blade shape; Step 6.3: Repeat steps 6.1 and 6.2 until the airfoil profile coordinates after all locations on the clean airfoil have accumulated dirt are obtained; Step 6.4: Smoothly connect all the scale coordinates of each modeling result to obtain the outline of the scale blade shape.

Images