Blade modal characteristic identification method considering blade front edge unsteady cavitation morphology

Abstract

The invention discloses a blade modal characteristic identification method considering the unsteady cavitation morphology of the front edge of a blade, and relates to the field of hydraulic mechanical dynamics, and the method comprises the steps: carrying out the unsteady calculation considering the phase change and cavitation of different working conditions of a flow field surrounding a blade, obtaining a flow field simulation result, and extracting the cavitation morphology at N moments; constructing and optimizing an initial cavitation domain three-dimensional digital model; performing spatial hierarchical Boolean operation on the optimized cavitation domain three-dimensional digital model to generate a hierarchical cavitation region with gradient distribution characteristics; endowing each layered area with a corresponding equivalent acoustic attribute; setting a multi-intersection interface boundary condition in the fluid-solid coupling system of the layered cavitation region to obtain a coupling system with a dynamic multi-phase boundary; based on the system, a modal analysis method is adopted to solve a control equation, the vibration mode and the inherent frequency of the blade under different cavitation forms are calculated and output, and the real vibration mode and the inherent frequency of the blade under the cavitation condition can be quantitatively analyzed more accurately.

Description

Technical Field

[0001] This application relates to the field of hydraulic machinery dynamics, and in particular to a method for identifying blade modal characteristics that takes into account the unsteady cavitation morphology of the blade leading edge. Background Technology

[0002] Cavitation is a typical flow characteristic of airflow around blades at non-design angles of attack or flow velocities. The resulting cavitation collapse and regeneration cycle significantly alters the dynamic characteristics of fluid-structure coupled systems. When cavitation develops to a critical state, the phase distribution and acoustic parameters of the fluid domain undergo abrupt changes, leading to a fundamental shift in the modal characteristics of the hydrofoil. Accurately quantifying the impact of cavitation morphology on natural frequencies and added mass is a core prerequisite for predicting resonance risk and optimizing structural design.

[0003] When the blade operates at a constant flow rate, the decrease in the cavitation number σ becomes the core control parameter for cavitation evolution. At different cavitation numbers, the morphology and volume of cavitation clouds on the blade surface vary. Furthermore, after the initial formation of cavitation, periodic shedding occurs, altering the instantaneous geometry of the cavitation clusters on the blade surface. The expansion of the cavitation region reduces the fluid's added mass, inevitably affecting the blade's structural dynamics.

[0004] For engineering equipment such as blades and turbines with blade structures, current modal analysis based on pure water conditions yields the mode shapes and natural frequencies of the solid itself. However, for blades subjected to different cavitation conditions, the misalignment analysis method based solely on structural dynamics studies in pure water may fail. Therefore, this paper proposes a method for analyzing the modal characteristics of turbine runners that integrates cavitation topology evolution and multiphase acoustic modeling. This method can more accurately and quantitatively analyze the true mode shapes and natural frequencies of blades under cavitation conditions. Summary of the Invention

[0005] The purpose of this application is to provide a method for identifying blade modal characteristics that takes into account the unsteady cavitation morphology of the blade leading edge, which can more accurately and quantitatively analyze the true vibration mode and natural frequency of the blade under cavitation conditions.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] This application provides a method for identifying blade modal characteristics considering unsteady cavitation morphology at the blade leading edge, including:

[0008] S1: Unsteady calculations considering phase change and cavitation are performed on the flow field around the blade under different operating conditions to obtain the flow field simulation results;

[0009] S2: Extract the cavitation morphology at N time points from the flow field simulation results;

[0010] S3: Geometrically reconstruct the cavitation morphology at the N time points to construct an initial three-dimensional digital model of the cavitation domain;

[0011] S4: optimizing the initial cavitation domain three-dimensional digital model through a geometric iteration and smoothing algorithm;

[0012] S5: based on the cross-sectional gas volume fraction distribution cloud chart in the flow field simulation result, dividing a plurality of layered intervals along a direction from a blade leading edge to a trailing edge, and performing a spatial layered Boolean operation on the optimized cavitation domain three-dimensional digital model according to a gas volume fraction threshold value corresponding to each layer to generate a layered cavitation zone with gradient distribution characteristics;

[0013] S6: based on the gas volume fraction of the layered cavitation zone, calculating a mixture density of each layer by using a porosity formula, and combining a gas-water mixture sound speed model to determine an equivalent sound speed of each layer, and establishing a porosity-sound speed correlation relationship to give each layered region a corresponding equivalent acoustic property;

[0014] S7: in a fluid-structure coupling system including a solid blade, an external water flow domain, and the layered cavitation zone having been given a corresponding equivalent acoustic property, setting a multiphase interface boundary condition to obtain a coupling system with a dynamic multiphase boundary; the multiphase interface boundary condition includes: setting a full absorption boundary for a gas-liquid interface, and setting a dynamically adjusted impedance boundary for a gas-solid interface;

[0015] S8: based on the coupling system with the dynamic multiphase boundary, solving a mass matrix, a damping matrix, and a stiffness matrix control equation by using a modal analysis method to calculate and output a vibration mode and a natural frequency of the blade under different cavitation forms.

[0016] Optionally, the optimization of the initial cavitation domain three-dimensional digital model through the geometric iteration and smoothing algorithm specifically includes:

[0017] calculating a volume coincidence rate, a surface area coincidence rate, a Hausdorff distance, and a root mean square of surface distance;

[0018] based on the volume coincidence rate, the surface area coincidence rate, the Hausdorff distance, and the root mean square of surface distance, iteratively optimizing the initial cavitation domain three-dimensional digital model according to a preset rate limit until all rate conditions are met to obtain an optimized cavitation domain three-dimensional digital model; the preset rate limit includes: volume coincidence rate ≥ 99%, surface area coincidence rate ≥ 99%, Hausdorff distance ≤ 1 mm, and root mean square of surface distance ≤ 0.12 mm.

[0019] Optionally, the blade modal characteristic identification method considering the unsteady cavitation form of the blade leading edge further includes, between step S4 and step S5:

[0020] calculating a volume rate limit value based on the volume coincidence rate, the surface area coincidence rate, the Hausdorff distance, and the root mean square of surface distance;

[0021] determine the quality of fit based on the volume ratio value.

[0022] Optionally, the expression of the volume fit ratio is as follows:

[0023]

[0024] wherein V cr is the volume fit ratio, V smooth is the smoothed volume, V original is the original model volume after CFD post-processing;

[0025] The expression of the surface area fit ratio is as follows:

[0026]

[0027] wherein S acr is the surface area fit ratio, S smooth is the smoothed surface area, S original is the original surface area.

[0028] Optionally, the expression of the Hausdorff distance is as follows:

[0029] H d (A,B) = max{sup_{a∈A}inf_{b∈B}d(a,b),

[0030] sup_{b∈B}inf_{a∈A}d(b,a)}.

[0031] wherein A, B are the original model surface point set and the smoothed model surface point set, H d (A, B) is the Hausdorff distance between point A and point B, sup is the minimum upper bound, inf is the maximum lower bound, a is a point in the upper surface point set, and b is a point in the lower surface point set.

[0032] Optionally, the expression of the root mean square of the distance between surfaces is as follows:

[0033]

[0034] wherein N is the number of points sampled on the original surface S original , p i is the i-th sampling point, d(p i , S smooth ) is the nearest point distance of p i to the smoothed surface S smooth , and sqrt is the square root symbol.

[0035] Optionally, the expression of the volume ratio value is as follows:

[0036]

[0037] where V cr is the volume overlap ratio, S acr is the surface overlap ratio, H d (A, B) is the Hausdorff distance, and RMSD is the root mean square distance between surfaces.

[0038] Optionally, the absorption coefficient in the perfectly matched layer is α, and the formula is as follows:

[0039]

[0040] where R t is the ratio of the thickness of the cavitation zone to the thickness of the blade.

[0041] Optionally, the calculation formula of the dynamic impedance boundary is as follows:

[0042]

[0043] where (Z real , Z imag ) is the dynamic impedance boundary, R t is the ratio of the thickness of the cavitation zone to the thickness of the blade.

[0044] Optionally, the expression of the mass matrix, the damping matrix, and the stiffness matrix control equation is as follows:

[0045]

[0046] where M S is the structure mass matrix, is the fluid density, R L is the liquid acoustic boundary matrix, T represents transposition, M L is the liquid mass matrix, R L,G is the liquid-gas interface matrix, M G is the gas mass matrix, is the structure displacement vector, is the liquid acoustic pressure vector, is the gas acoustic pressure vector, C S is the structure damping matrix, C L is the liquid damping matrix, C G is the gas damping matrix, is the structure displacement vector, is the fluid acoustic pressure vector, is the gas acoustic pressure vector, K S is the structure stiffness matrix, K L is the liquid stiffness matrix, R GK is the gas acoustic boundary matrix, G K is the gas stiffness matrix, u S u is the structure displacement, p L p is the liquid acoustic pressure, G p is the gas acoustic pressure, F S F is the structure external load, L F is the, G F is the gas external load, the subscripts S, L and G represent the structure, liquid and gas respectively, and p represents the acoustic pressure.

[0047] According to the specific embodiments provided in the application, the application has the following technical effects:

[0048] The application provides a blade modal characteristic identification method considering unsteady cavitation patterns of a blade leading edge, comprising: performing unsteady calculation considering phase change and cavitation on different working conditions of a blade circumferential flow field, and extracting cavitation patterns at N time points in the calculation results; geometrically reconstructing the cavitation patterns to establish a three-dimensional digital model of a cavitation domain; optimizing the cavitation model, optimizing the topological structure of the cavitation domain to fit the physical cavitation patterns through geometric iteration and smoothing algorithm; according to the gas phase distribution law of the cavitation area, the reconstructed cavitation domain is discretely characterized by spatial layering; a porosity-acoustic velocity correlation model is established, and the cavitation domain is given equivalent acoustic properties (acoustic velocity, density) in different zones; a dynamic rating method of gas-liquid / gas-solid interface is added in the fluid-solid coupling system to characterize the interaction mechanism of the multiphase medium; finally, the mode analysis method is used to calculate the vibration mode and natural frequency of the blade under different cavitation patterns. The application can realize high-precision prediction of the vibration characteristics of the blade under unsteady cavitation conditions, and the finally calculated vibration mode and natural frequency can more truly reflect the dynamic response of the blade in the complex cavitation flow field in actual operation, thereby providing accurate data for the fatigue life prediction, vibration noise evaluation and stability design of the impeller, and effectively preventing resonance, fatigue fracture and other structural damage hazards induced by cavitation. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0050] Figure 1 Fig. 1 is a flowchart of a blade modal characteristic identification method considering unsteady cavitation patterns of a blade leading edge according to an embodiment of the application;

[0051] Figure 2 Fig. 2 is a schematic diagram of a cavitation pattern at a certain time extracted from the post-processing results of fluid simulation of a blade circumferential flow field according to an embodiment of the application.

[0052] Figure 3 For an embodiment of the present application, the extracted cavitation morphology is introduced into a three-dimensional modeling software for closure to construct a three-dimensional digital model schematic diagram;

[0053] Figure 4 For an embodiment of the present application, the steam geometry model is iterated based on the volume fitting rate formula, and the abnormal protrusions are smoothed and eliminated, as shown in the schematic diagram;

[0054] Figure 5 For an embodiment of the present application, the optimized model is reverse-modeled to generate a geometric entity, as shown in the schematic diagram;

[0055] Figure 6 For an embodiment of the present application, the cavitation morphology of the blade surface is spatially layered according to the cross-sectional gas phase distribution rule, and the reconstructed cavitation domain is shown in the schematic diagram;

[0056] Figure 7 For an embodiment of the present application, the calculation domain of the blade and the external flow field fluid-solid coupling is shown in the schematic diagram;

[0057] Figure 8 For an embodiment of the present application, the vibration mode of the blade in the first order water mode under a certain cavitation condition is shown in the schematic diagram. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0059] The above purposes, features and advantages of the present application can be more obvious and easy to understand. The present application will be described in further detail below with reference to the drawings and specific embodiments.

[0060] In one exemplary embodiment, as shown in Figure 1 A blade modal characteristic identification method considering unsteady cavitation morphology of blade leading edge is provided, which is executed by a computer device, specifically, can be executed by a terminal or a server, or can be executed by a terminal and a server together. In the embodiments of the present application, the method includes the following steps. Wherein:

[0061] S1: performing unsteady calculation considering phase change and cavitation on different working conditions of the blade circumferential flow field to obtain flow field simulation results.

[0062] S2: extracting cavitation morphology at N time points from the flow field simulation results.

[0063] Specifically, in this embodiment, firstly, based on CFD simulation technology, the unsteady cavitation flow calculation of NACA 0009 hydrofoil under different cavitation number conditions (for example, cavitation number 1.04, 1.66, 2.02, 5, etc., and any condition that causes cavitation is within the protection scope of this embodiment) is carried out. The chord length, span width and trailing edge thickness of the hydrofoil are 70 mm, 67 mm and 2.25 mm respectively. The material of the hydrofoil is aluminum alloy, and the density, Young's modulus and Poisson's ratio are 2700 kg / m 3 , 69 GPa and 0.334 respectively. The hydrofoil is horizontally installed in a water tunnel with a size of 700*70*190 mm, one side is fixed and the other side is free. The attack angle is 10 degrees, and the tip clearance is 3 mm. Based on the CFD unsteady cavitation simulation results, the cavitation morphology at N time points in a period is extracted, and the equal value surface cavity with a gas phase volume fraction a v = 0.001 is taken (see Figure 2 , Figure 2 The unsteady calculation of the flow field around the hydrofoil is carried out in the fluid simulation software, and different morphologies of cavitation cavities attached to the surface of the hydrofoil are obtained in the post-processing software.

[0064] S3: Geometric reconstruction of the N time points of cavitation morphology to construct an initial cavitation domain three-dimensional digital model.

[0065] Specifically, the CFD-derived STL format cavitation cavity is imported into a three-dimensional geometric modeling software for repair operations such as surface repair and bridge repair to complete the closure processing of the cavity and construct a complete cavitation domain digital three-dimensional model, i.e. the initial cavitation domain three-dimensional digital model. See Figure 3 .

[0066] S4: Optimizing the initial cavitation domain three-dimensional digital model by geometric iteration and smoothing algorithm.

[0067] Based on the initial cavitation domain three-dimensional digital model constructed in step S3, the geometric iteration and smoothing algorithm is used for topology optimization, which specifically includes: calculating the volume coincidence rate V cr , the surface area change rate S acr , the Hausdorff distance H(A, B) and the root mean square of surface distance RMSD, and taking V cr ≥ 99%, S acr ≥ 99%, H(A, B) ≤ 1 mm and RMSD ≤ 0.12 mm as the convergence criteria, iteratively optimizing the model geometry until all the rated conditions are met, to obtain the optimized cavitation domain geometric entity model. See Figure 4 , Figure 4 The steam geometric model is iterated based on the volume coincidence rate formula, and the model with abnormal protrusions is smoothed.

[0068] That is, the volume geometric coincidence rate V cr, the closed cavitation domain model after smoothing, the iteration method is at least rated range V cr ≥99%;

[0069] Surface area change rate S acr , the surface area change rate caused by direct reaction before and after smoothing, which is very important to emphasize the surface properties in fluid mechanics simulation, the iteration rate limit S acr ≥99%;

[0070] H ausdorff The maximum mismatch between the surface point set of the model after smoothing and the original STL cavity surface model is measured, the distance from any point on one surface to the nearest point on the other surface is calculated, and then the maximum value of these distances is taken, (one-way H ausdorff ), usually take the maximum value of two directions (two-way H ausdorff ) as the final measurement as shown in equation 3, for this value, based on the position coordinates of the grid nodes in the digital model before and after optimization, the coordinates that meet the iteration rate limit H(A,B)≤1mm are fixed, and the area that does not meet the area is further optimized and iterated. This rate limit method captures the maximum local deviation and can clearly indicate where the smoothed model deviates from the original model the farthest. The iteration rate limit is set to H(A,B)≤1mm; Root mean square surface distance, calculate the distance from a large number of points sampled on the original model surface to the nearest point on the smoothed model surface, then calculate the root mean square value of these distances (RMSD) to reflect the overall average deviation, the iteration rate limit is set to RMSD≤0.12mm.

[0071] Volume fit rate formula, the iteration limit can be set to:

[0072]

[0073] In the formula, V cr is the volume ratio, V smooth is the volume after smoothing, V original is the original model volume after CFD post-processing.

[0074] Surface area fit rate formula, the iteration limit can be set to:

[0075]

[0076] In the formula, S acr is the volume ratio, S smooth is the surface area after smoothing, S original is the original surface area.

[0077] The maximum value of the nearest distance between the surfaces before and after smoothing, Hausdorff distance method rate, first discretize the point cloud before and after optimization:

[0078] A = {k = 1,..., N}; B = {l = 1,..., M}:

[0079] Calculate Hausdorff distance H d :

[0080] H d (A, B) = max{sup_{a∈A}inf_{b∈B}d(a, b), sup_{b∈B}inf_{a∈A}d(b, a)}(3)

[0081] In the formula, A and B are the original model surface point set and the smoothed model surface point set, H d (A, B) is the Hausdorff distance between points A and B; sup is the supremum (the smallest upper bound), and inf is the infimum (the largest lower bound).

[0082] The root mean square of the distance between the surfaces is:

[0083]

[0084] In the formula, N is the number of points sampled on the original surface S original , p i is the i-th sampling point, d(p i , S smooth ) is the nearest point distance of point p i to the smoothed surface S smooth .

[0085] S5: Based on the cross-sectional gas phase volume fraction distribution cloud diagram in the flow field simulation result, a plurality of layered intervals are divided along the direction from the blade leading edge to the trailing edge, and a spatial layered Boolean operation is performed on the optimized cavitation domain three-dimensional digital model according to the corresponding gas phase volume fraction threshold of each layer, to generate a layered cavitation area with gradient distribution characteristics.

[0086] S6: Based on the gas phase volume fraction of the layered cavitation area, the mixture density of each layer is calculated using the porosity formula, and the equivalent sound speed of each layer is determined by combining the gas-water mixture sound speed model, to establish the porosity-sound speed correlation relationship, and to give each layered area corresponding equivalent acoustic properties.

[0087] Specifically, according to the cross-section gas volume fraction distribution cloud diagram in CFD-POST, a cross-section line is taken on the cloud diagram, the volume fraction value on the cross-section line is output, each layer is divided according to the level number, the distance of each layer is given, and the reconstructed geometry is subjected to Boolean operation and layering processing in three-dimensional software according to the layering distance: two target entities are subjected to set operation, and a boundary representation method (B-rep) is used to describe, that is, the boundary is defined by points (Vertices), edges (Edges) and faces (Faces). For example, given level = 0.1 steam body 1 and internal level = 0.5 steam body 2, a new entity C is generated, and the spatial region of the new entity C satisfies:

[0088] Union (A∪B): C = {points in A OR points in B}

[0089] Subtraction (A-B): C = {points in A AND NOT points in B}

[0090] Intersection (A∩B): C = {points in A AND points in B}

[0091] The mixture density is calculated based on the porosity calculation formula of the processed geometry, and the mixed phase sound speed is given according to the gas-water mixed phase sound speed formula, and the multiphase sound speed correlation modeling is carried out, and the material properties (sound speed, density) are set in the partition. For details, see Figure 6 The results of the reconstructed geometry after layering processing according to the CFD-POST post-processing results are shown in the schematic diagram of the flow field cross-section and the gas volume fraction cloud distribution.

[0092] Porosity formula:

[0093]

[0094] Where, α porosity, V G is the gas volume, V is the cavity volume, ρ c is the mixture density, ρ L is the water phase density, ρ G is the gas density, and subscript G represents gas.

[0095] The relationship between the sound speed c in the gas-water mixture and the air volume fraction α:

[0096]

[0097] Where, c is the sound speed, k = 1, k = 1.4 is the isothermal and adiabatic state, and p is the sound pressure.

[0098] S7: In the fluid-structure coupling system containing the solid blade, the external water flow field, and the layered cavitation region with the corresponding equivalent acoustic properties, a multi-phase interface boundary condition is set to obtain a coupling system with a dynamic multi-phase boundary; the multi-phase interface boundary condition includes: setting a full absorption boundary for the gas-liquid interface, and setting a dynamically adjusted impedance boundary for the gas-solid interface.

[0099] Referring to Figure 7 , the cavitation domain + solid domain + water flow field is reverse-modeled, a new flow field is constructed by Boolean operation, and is imported into modal analysis software as an initial condition, and material composition and boundary conditions are further set.

[0100] For solid-liquid, solid-gas, and gas-liquid contact areas, the gas-liquid and gas-solid coupling interfaces are set on the basis of the traditional fluid-structure coupling interface, which is expanded on the basis of the traditional fluid-structure coupling interface, and the absorption coefficient of the gas-solid and gas-liquid interface is dynamically adjusted according to the thickness change of the cavitation region. First, the gas-liquid interface is set as a full absorption surface, the fluid-structure interface is set as a standard FSI, and the dynamic absorption coefficient mechanism is to dynamically update the absorption coefficient a according to the ratio R of the cavitation region thickness δ to the blade thickness t. t t > N t When R t > 3, set it as full absorption a = 1, 1 < R t < 3, set it as medium absorption a = 0.5, and when 0.1 < R t < 1, set it as a linear transition zone, a = 0.1 + 0.4 * (R t - 0.1) / 0.9. When the ratio is less than 0.1, take a = 0.1 minimum absorption. For the gas-solid interface, a dynamically adjusted impedance boundary is set, when R t > 5.0, the acoustic resistance Z real = 50 is in the super-cavitation state, the low resistance (the sound wave is easy to penetrate) 2 < ratio < 5, Z real = 80 + 20 * (R t - 2) increases with the increase of cavitation, when 0.5 < R t < 2, Z real = 200 + 300 * (2.0 - R t ) increases with the decrease of cavitation, and other Z real = 1000 + 1500 * (0.5 - R t ) is the high resistance of the non-cavitation region. When the dynamic acoustic resistance R t > 5.0, Z imag = 0 has no phase shift, when R t > 2.0, Z imag = -10 * (Rt-2) is a small negative resistance, and when R t > 0.5: Z imag ​= -50 - 100 * (2.0 - R t ), strong negative reactance; other no cavitation when Z imag = -400 - 600 * (0.5 - R t ), very strong negative reactance.

[0101] The absorption coefficient a is determined by the value of R t :

[0102]

[0103] The formula of dynamic impedance boundary (Z real , Z imag ):

[0104]

[0105]

[0106] These new interfaces make the control equations more complex, and the specific form is as follows:

[0107]

[0108] Where, M S is the structure mass matrix, is the fluid density, R L is the liquid acoustic boundary matrix, T represents transposition, M L is the liquid mass matrix, R L,G is the liquid-gas interface matrix, M G is the gas mass matrix, is the structure displacement vector, is the liquid acoustic pressure vector, is the gas acoustic pressure vector, C S is the structure damping matrix, C L is the liquid damping matrix, C G is the gas damping matrix, is the structure displacement vector, is the fluid acoustic pressure vector, is the gas acoustic pressure vector, K S is the structure stiffness matrix, K L is the liquid stiffness matrix, R G is the gas acoustic boundary matrix, K G is the gas stiffness matrix, u S is the structure displacement, p L is the liquid acoustic pressure, p G is the gas acoustic pressure, F S is the structure external load, F L is, F GFor the gas external load, the subscripts S, L and G represent structure, liquid and gas respectively, and p represents sound pressure.

[0109] S8: based on the coupling system with dynamic multiphase boundary, a modal analysis method is used to solve the mass matrix, damping matrix and stiffness matrix control equation, and the vibration mode and natural frequency of the blade under different cavitation modes are calculated and output.

[0110] Based on the modal analysis method, the vibration mode and natural frequency of the hydrofoil under different cavitation modes are finally calculated, which are compared with the natural frequency of the hydrofoil in air and the natural frequency of the hydrofoil in pure water. The first-order bending mode natural frequency of the hydrofoil in air f air = 399.7 Hz, the first-order bending mode natural frequency of the hydrofoil in pure water f water = 211.6 Hz, under a certain cavitation condition, considering the first-order bending natural frequency of the hydrofoil with cavitation mode attached to the hydrofoil in water f vapor = 265 Hz, which is 25.6% higher than the natural frequency of the hydrofoil in pure water.

[0111] As shown in Figure 8 , the first-order in-water modal shape considering cavitation mode is obtained through modal analysis, and the displacement of each node is output, with an amplitude of 4.03e-6 m.

[0112] In another exemplary embodiment of the present application, in order to evaluate the fitting quality of the model, steps S4 and S5 further include:

[0113] Based on the volume fitting rate, surface area fitting rate, Hausdorff distance and root mean square of surface distance, the volume rate constant value is calculated;

[0114] Based on the volume rate constant value, the fitting quality is determined.

[0115] The specific formula is as follows:

[0116]

[0117] The present application proposes a calculation formula of the volume rate constant value C. Using this formula, the cavitation model used for calculation is geometrically reconstructed, and the fitting quality is evaluated. When C≥1, it means that all conditions are met, C>1 means higher fitting rate; C<1 means that the conditions are not fully met, and the volume A in the CFD calculation result is iteratively optimized to volume B through the volume rate setting method, see Figure 5 The final inverse modeling schematic diagram is shown in The final inverse modeling schematic diagram is shown in

[0118] Any technical features in the above embodiments can be combined, and for the sake of brevity, not all possible combinations are described above, however, it should be understood that the application encompasses all possible combinations of the technical features described above.

[0119] The principles and implementation manners of the present application are described herein by using specific examples, and the above embodiments are only used to help understand the method of the present application and its core idea; meanwhile, according to the idea of the present application, the specific implementation manners and application scopes will be changed by those skilled in the art. In conclusion, the content of the present specification should not be understood as a limitation of the present application.

Claims

1. A blade modal characteristic identification method considering blade leading edge unsteady cavitation pattern, characterized in that, The blade modal characteristic identification method considering the unsteady cavitation shape of the blade leading edge comprises: S1: performing unsteady calculation considering phase change and cavitation on different working conditions of the blade circumferential flow field to obtain flow field simulation results; S2: extracting cavitation shapes at N time points from the flow field simulation results; S3: geometrically reconstructing the cavitation shapes at the N time points to construct an initial cavitation domain three-dimensional digital model; S4: optimizing the initial cavitation domain three-dimensional digital model through a geometric iteration and smoothing algorithm; S5: based on the cross-sectional gas volume fraction distribution cloud diagram in the flow field simulation results, dividing multiple layered intervals along the direction from the blade leading edge to the trailing edge, and performing spatial layered Boolean operation on the optimized cavitation domain three-dimensional digital model according to the gas volume fraction threshold of each layer to generate a layered cavitation zone with gradient distribution characteristics; S6: based on the gas volume fraction of the layered cavitation zone, calculating the density of each layer of the mixture by using a porosity formula, and combining a gas-water mixture sound speed model to determine the equivalent sound speed of each layer, thereby establishing a porosity-sound speed correlation relationship to give each layered region corresponding equivalent acoustic properties; S7: in a fluid-structure coupling system comprising a solid blade, an external water flow domain and the layered cavitation zone having given corresponding equivalent acoustic properties, setting a multiphase interface boundary condition to obtain a coupling system with a dynamic multiphase boundary; the multiphase interface boundary condition comprises: setting a full absorption boundary for the gas-liquid interface and a dynamically adjusted impedance boundary for the gas-solid interface; S8: based on the coupling system with the dynamic multiphase boundary, solving the mass matrix, damping matrix and stiffness matrix control equation by using a modal analysis method to calculate and output the vibration mode and natural frequency of the blade under different cavitation shapes.

2. The blade modal characteristic identification method considering the blade leading edge unsteady cavitation pattern according to claim 1, characterized in that, The optimization of the initial cavitation domain three-dimensional digital model through the geometric iteration and smoothing algorithm specifically comprises: calculating the volume coincidence rate, surface area coincidence rate, Hausdorff distance and root mean square of the surface distance; based on the volume coincidence rate, surface area coincidence rate, Hausdorff distance and root mean square of the surface distance, iteratively optimizing the initial cavitation domain three-dimensional digital model according to a preset rate limit until all rate conditions are met to obtain the optimized cavitation domain three-dimensional digital model; the preset rate limit comprises: volume coincidence rate ≥ 99%, surface area coincidence rate ≥ 99%, Hausdorff distance ≤ 1 mm, and root mean square of the surface distance ≤ 0.12 mm.

3. The blade modal characteristic identification method considering the blade leading edge unsteady cavitation pattern according to claim 2, characterized in that, The blade modal characteristic identification method considering the unsteady cavitation shape of the blade leading edge further comprises, between step S4 and step S5: calculating a volume rate limit value based on the volume coincidence rate, surface area coincidence rate, Hausdorff distance and root mean square of the surface distance; determining a coincidence quality based on the volume rate limit value.

4. The blade modal characteristic identification method considering the blade leading edge unsteady cavitation pattern according to claim 2, characterized in that, The expression of the volume coincidence rate is as follows: Where V cr is the volume fit rate, V smooth is the smoothed volume, V original is the original model volume after CFD post-processing; The expression of the surface area coincidence rate is as follows: In the formula, S acr is the surface area fit ratio, S smooth is the smoothed surface area, S original is the original surface area.

5. The blade modal characteristic identification method considering the blade leading edge unsteady cavitation pattern according to claim 2, characterized in that, The expression of the Hausdorff distance is as follows: In the formula, A, B are the original model surface point set and the smoothed model surface point set, H d (A, B) is the Hausdorff distance between point A and point B, sup is the minimum upper bound, inf is the maximum lower bound, a is a point in the upper surface point set, and b is a point in the lower surface point set.

6. The method for blade modal characteristic identification considering blade leading edge unsteady cavitation pattern according to claim 2, characterized in that, The expression of the root mean square of the surface distance is as follows: where N is the number of points in the original surface S original the number of points to up-sample, p i is the ith sample point, d(p i , S smooth ) is the distance from p i to the nearest point on the smoothed surface S smooth sqrt is the square root.

7. The method for identifying blade modal characteristics considering unsteady cavitation morphology of blade leading edge according to claim 3, characterized in that, The expression of the volume rate limit value is as follows: where V cr is the volume overlap, S acr is the surface area overlap, H d (A, B) is the Hausdorff distance, and RMSD is the root mean square distance between surfaces.

8. The method for blade modal characteristic identification considering blade leading edge unsteady cavitation pattern according to claim 1, characterized in that, The absorption coefficient in the full absorption boundary is α, and the formula is as follows: wherein R t is the ratio of cavitation zone thickness to blade thickness.

9. The method for blade modal characteristic identification considering unsteady cavitation morphology of blade leading edge according to claim 1, characterized in that, The calculation formula of the dynamically adjusted impedance boundary is as follows: where (Z real imag ) is a dynamic impedance boundary, R t is the ratio of the cavitation zone thickness to the blade thickness.​ 10. The method for blade modal characteristic identification considering unsteady cavitation morphology of blade leading edge according to claim 1, characterized in that, The mass matrix, damping matrix and stiffness matrix control equation expression as follows: where M S is the structural mass matrix, is the fluid density, R L is the liquid acoustic boundary matrix, T denotes transpose, M L is the liquid mass matrix, R L,G is the liquid-gas interface matrix, M G is the gas mass matrix, is the structural displacement vector, is the liquid acoustic pressure vector, is the gas acoustic pressure vector, C S is the structural damping matrix, C L is the liquid damping matrix, C G is the gas damping matrix, is the structural displacement vector, is the fluid acoustic pressure vector, is the gas acoustic pressure vector, K S is the structural stiffness matrix, K L is the liquid stiffness matrix, R G is the gas acoustic boundary matrix, K G is the gas stiffness matrix, u S is the structural displacement, p L is the liquid acoustic pressure, p G is the gas acoustic pressure, F S is the structural external load, F L is the, F G is the gas external load, the subscripts S, L, and G represent the structure, liquid, and gas, respectively, and p denotes acoustic pressure.

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