Elastic material hydrofoil fluid-solid coupling cavitation erosion forecasting method based on potential energy theory

Abstract

The invention discloses an elastic material hydrofoil fluid-solid coupling cavitation erosion forecasting method based on a potential energy theory, and belongs to the field of computational fluid mechanics and cavitation. The implementation method comprises the following steps: simulating the cavitation of the hydrofoil made of the elastic material by using a tight coupling algorithm to obtain the pressure and steam volume fraction distribution of the surface of the hydrofoil; a steam volume fraction distribution based on pressure; constructing an erosion index correction factor F for representing the bending torsional deformation degree of the elastic material hydrofoil to correct the cavitation erosion index represented by the pressure wave power density; the cavitation erosion indexes larger than a threshold value are screened out, and the final cavitation erosion risk index is a quotient after superposition of the cavitation erosion indexes; the corrected cavitation erosion index data are interpolated into RGB color data, the data serve as a geometric structure model of a fourth-dimensional mapping elastic material hydrofoil, and the corrected cavitation erosion index numerical value is represented through color change. The corrected cavitation erosion index can more accurately forecast a cavitation erosion risk part on the surface of the hydrofoil made of the elastic material.

Description

Technical Field

[0001] The present invention belongs to the fields of computational fluid dynamics and cavitation, and relates to a method for predicting fluid-structure interaction cavitation erosion of an elastic material hydrofoil based on potential energy theory. Background Art

[0002] Computational Fluid Dynamics (CFD) has emerged as an interdisciplinary field between mathematics, fluid mechanics, and computer science since the 1950s with the development of computers. Its main research content is to solve the governing equations of fluid mechanics through computers and numerical methods to simulate and analyze fluid mechanics problems.

[0003] Cavitation refers to the phenomenon of generating bubbles or bubble clusters when the pressure in a liquid drops to a sufficiently low level under certain conditions. When the pressure in the liquid drops to a certain value, cavities filled with gas and vapor will be generated in the liquid. These cavities may be single spherical bubbles, bubble clusters formed by the accumulation of multiple bubbles, or cavities with irregular shapes. Cavitation can produce physical effects such as local high temperature and pressure, shock waves, and microjets. Cavitation may lead to the deterioration of the hydrodynamic performance of moving objects, cavitation damage to structural materials, and cause vibration and increased noise.

[0004] Cavitation erosion refers to the situation in a flowing liquid where, when the pressure in a local area suddenly drops below the vaporization pressure corresponding to the liquid temperature in that area for some reason, part of the liquid vaporizes, and the gas dissolved in the liquid escapes, forming bubbles (or cavities) in the liquid flow. When the cavities enter an area with a higher pressure along with the liquid flow, they lose the conditions for existence and suddenly collapse. The movement of the liquid around the original cavities causes the pressure in the local area to increase suddenly. If continuously formed and growing cavities in the liquid flow frequently collapse near the solid wall surface, the wall surface will be repeatedly impacted by huge pressures, thereby causing fatigue damage or even surface erosion of the material. Cavitation erosion may lead to material damage, vibration, noise, and performance degradation. Therefore, predicting the occurrence of cavitation erosion is of great significance for the optimization of structures.

[0005] The mechanism of this cavitation erosion is based on the concept of energy cascade proposed by Fortes-Patella et al. It is believed that when the macroscopic-scale cavity cloud collapses, the potential energy will be converted into acoustic energy and radiated outward. When this energy propagates to the vicinity of micro-cavities near the wall surface, it will break the energy balance inside and outside the cavities in the quasi-steady state, causing these micro-cavities to burst inward to form microjets or shock waves that impact the material surface. This shock wave will propagate to the solid surface and cause an impact on the material, thereby forming cavitation erosion.

[0006] This method requires obtaining the environmental pressure field p that drives the cavity to collapse f, However, it is extremely difficult to accurately predict this pressure field in the cavitation field and requires a large amount of computing resources. Therefore, most researchers use the instantaneous pressure p instead of p f , which greatly simplifies the calculation. However, under this simplification, the prediction results of the cavitation erosion performance near the leading edge of the blade are not good. When using the instantaneous pressure to estimate the ambient pressure p f , the pressure inside the cavitation cluster is almost equal to p v , which means that the pressure difference calculated by this method may be very close to zero. To more accurately evaluate the ambient pressure field p f , Melissaris et al. suggested using the mean pressure field to predict the erosion risk, and the erosion distribution obtained from the mean pressure field is more consistent with the experimental results. Inspired by this idea, this method adopts a similar treatment and uses the mean pressure field result to replace the ambient pressure field p v for erosion assessment. Summary of the Invention

[0007] The object of the present invention is to provide a fluid-structure interaction cavitation prediction method for elastic material hydrofoils based on potential energy theory. The cavitation of elastic material hydrofoils is simulated using a tightly coupled algorithm in the System Coupling module of the Ansys Workbench platform to obtain the pressure and vapor volume fraction distributions on the hydrofoil surface; based on the pressure and vapor volume fraction distributions, a cavitation erosion index characterized by the pressure wave power density is obtained; since the elastic material hydrofoil will bend and twist under the impact force generated by the collapse of the cavity, which in turn affects the intensity of the shock wave generated by the subsequent cavity collapse, an erosion index correction factor F for characterizing the degree of bending and twisting deformation of the elastic material hydrofoil is constructed, and the cavitation erosion index characterized by the pressure wave power density is corrected according to the erosion index correction factor F. The corrected cavitation erosion index can more accurately predict the cavitation risk sites on the surface of the elastic material hydrofoil, that is, improve the accuracy of the fluid-structure interaction cavitation prediction of the elastic material hydrofoil based on potential energy theory.

[0008] The object of the present invention is achieved by the following technical solutions:

[0009] A method for predicting fluid-structure interaction cavitation of an elastic material hydrofoil based on potential energy theory disclosed by the present invention uses a tightly coupled algorithm to simulate the cavitation of the elastic material hydrofoil in the System Coupling module of the Ansys Workbench platform, and obtains the pressure and vapor volume fraction distributions on the hydrofoil surface; based on the pressure and vapor volume fraction distributions, a cavitation erosion index characterized by the pressure wave power density is obtained; an erosion index correction factor F for characterizing the degree of bending and torsional deformation of the elastic material hydrofoil is constructed to correct the cavitation erosion index characterized by the pressure wave power density; the cavitation erosion indexes greater than the threshold are screened out, and the final cavitation risk index is the quotient after their superposition; the corrected cavitation erosion index data is interpolated into the RGB color data, and this data is used as the fourth dimension to map into the geometric structure model of the elastic material hydrofoil, and the magnitude of the corrected cavitation erosion index is characterized by color change. The corrected cavitation erosion index can more accurately predict the cavitation risk positions on the surface of the elastic material hydrofoil, that is, the accuracy of predicting the fluid-structure interaction cavitation of the elastic material hydrofoil is improved based on the potential energy theory.

[0010] A method for predicting fluid-structure interaction cavitation of an elastic material hydrofoil based on potential energy theory disclosed by the present invention includes the following steps:

[0011] Step 1, establish a three-dimensional flow domain and a hydrofoil geometric model, and perform mesh division on the three-dimensional flow domain and the hydrofoil respectively. Import the divided three-dimensional flow domain and hydrofoil meshes into the System Coupling module of the Ansys Workbench platform, perform initial steady-state flow field numerical calculation and fluid-structure interaction calculation of the unsteady flow field, and obtain a CSV table file of the pressure and vapor volume fraction distributions on the hydrofoil surface.

[0012] Step 2, calculate the CSV table file of the pressure and vapor volume fraction distributions at each node on the hydrofoil surface at each time step, use the first-order backward difference method to calculate the instantaneous vapor volume fraction, multiply the calculated vapor volume fraction and the pressure difference between the average pressure field and each node on the hydrofoil surface, and add a negative sign to the multiplication result to obtain a cavitation erosion index characterized by the pressure wave power density.

[0013] Step 3, since the elastic material hydrofoil will undergo bending and torsional deformation due to the impact force generated by the collapse of the cavity, which will in turn affect the intensity of the shock wave generated by the subsequent cavity collapse. Combining the shear modulus, Young's modulus and Poisson's ratio of the elastic material, an erosion index correction factor F for characterizing the degree of bending and torsional deformation of the elastic material hydrofoil is constructed. The product of the erosion index correction factor and the cavitation erosion index characterized by the pressure wave power density is the corrected cavitation erosion index at each position node.

[0014] Step 4: Based on the fatigue strength of the material itself and the cumulative effect of cavitation occurrence, when the corrected cavitation erosion index is greater than the threshold value, it is determined that the intensity of the shock wave will cause cavitation to the material on the surface of the hydrofoil. Based on this, the cavitation erosion index of each position node after correction is screened, and superposition is performed according to each time step. The result obtained by dividing the superposed result by the number of corrected cavitation erosion indices greater than the threshold value is the final cavitation risk index. The corrected cavitation erosion index can more accurately predict the cavitation risk on the surface of the elastic material hydrofoil.

[0015] It also includes Step 5: Interpolate the corrected cavitation erosion index data into the RGB color data, and map this data into the geometric structure model of the elastic material hydrofoil as the fourth dimension, using color change to characterize the numerical value of the corrected cavitation erosion index, and more significantly and accurately realizing the prediction of the cavitation risk area on the surface of the elastic material hydrofoil according to the color change.

[0016] The specific implementation method of Step 1 is as follows:

[0017] Step 1.1: Establish a three-dimensional basin and hydrofoil geometric model, and perform mesh division on the three-dimensional basin and hydrofoil respectively. The fluid domain mesh is divided into two parts. The part around the hydrofoil uses unstructured mesh, and at the same time, the near-wall mesh is encrypted. The outer domain mesh around the hydrofoil uses structured mesh to ensure that the mesh sizes at the interface with the inner domain mesh are the same.

[0018] Step 1.2: Set no-slip and smooth wall boundary conditions for both the surface of the elastic hydrofoil and the boundary of the three-dimensional basin, and set the surface of the elastic material hydrofoil as the fluid-structure interaction interface.

[0019] Step 1.3: Import the divided three-dimensional basin and hydrofoil meshes into the SystemCoupling module of the Ansys Workbench platform, perform initial steady-state flow field numerical calculation and fluid-structure interaction calculation of the unsteady flow field. Solve the initial value of the steady-state flow field according to the flow field control equations shown in Equations (1.1) and (1.2). Transfer the pressure and velocity data of the initial value of the steady-state flow field to the structural field through the fluid-structure interaction interface, and solve the finite element structural deformation of the structural field according to Equation (2) to obtain the finite element structural deformation.

[0020] The flow field control equations for calculating the fluid domain adopt the homogeneous flow model. To simplify the calculation process and improve the calculation speed, the relative velocity and interaction between the vapor / liquid phases are ignored. The flow field control equation set includes the continuity equation and the momentum equation:

[0021]

[0022] Among them, Denotes the partial derivative of the function with respect to the corresponding variable, ρ is the density of the fluid, t is the time, p is the pressure at the fluid inlet, u i 、u j represent the velocity components of the fluid, μ m and μ t are the laminar and turbulent viscosity coefficients of the fluid respectively, x i 、x j represent the position components of the fluid;

[0023] The structural field control equation (2) is:

[0024]

[0025] where, [M s , [C s , [K s are the mass matrix, damping matrix and stiffness matrix of the hydrofoil structure of the material respectively, {X} is the structural displacement, is the structural velocity, is the structural acceleration, {F CFD} represents the flow field force on the structure under the fluid-structure interaction, {F EX} represents the external excitation force on the structure under the fluid-structure interaction.

[0026] Step 1.4, transfer the information such as the structural field deformation to the unsteady flow field through the fluid-structure interaction interface, update the flow field grid and solve the flow field according to the structural deformation to obtain the flow field solution result;

[0027] Step 1.5, judge whether it converges according to the solution result of each sub-iteration step within each time step. If the requirement is met, directly enter the calculation of the next time step; if the requirement is not met, judge whether the number of sub-iteration steps is less than the maximum number of iteration steps. If the requirement is met, continue the sub-iteration convergence solution calculation. If the requirement is not met, enter the calculation of the next time step

[0028] Step 1.6, through continuous solution of each sub-iteration step within each time step, when the calculation converges, the fluid-structure interaction calculation is completed, and a CSV table file of the pressure and steam volume fraction distribution on the hydrofoil surface is output.

[0029] The specific implementation method of Step 2 is:

[0030] Step 2.1, the cavitation erosion index characterized by the pressure wave power density is the result derived based on the potential energy theory. The potential energy expression of the cavitation cloud is as follows:

[0031] E pot =ΔP·V v

[0032] In the above formula, ΔP = P f -Pv , where P f is the environmental pressure outside the cloud, and P v is the pressure inside the cloud, i.e., the saturated vapor pressure, and V v is the vapor volume.

[0033] The instantaneous power is the derivative of the potential energy with respect to time. Since the change rate of the vapor volume is one order of magnitude higher than the change rate of the pressure difference inside and outside the vapor, the term V v {d(ΔP) / dt} is ignored. Divide both sides of the equation by the total volume of the grid cells occupied by the cloud to obtain the instantaneous power p per unit volume in the cloud pot . The amplitude p wave of the pressure wave is proportional to . Use p pot to simplify and replace p wave to qualitatively estimate the erosion risk area. V cell is the volume of the cloud cavity, and α v is the vapor volume fraction. The instantaneous erosion load, i.e., the instantaneous pressure wave power density p pot is expressed as follows:

[0034]

[0035] The environmental pressure field p f is the pressure field that effectively drives the collapse of the cavity. However, it is extremely difficult to accurately predict this pressure field in the cavitation field and requires a large amount of computing resources. The average pressure field result is used to replace the environmental pressure field p f for erosion assessment. The pressure wave power density formula is modified as:

[0036]

[0037] If only the contraction process during cavitation is considered, then should be negative. That is, when the change rate of the vapor volume fraction around the vapor bubble with respect to time is less than zero, it is determined that the cavity on the surface of the hydrofoil is in the contraction stage, and its collapse result will cause cavitation erosion risk. To ensure that the cavitation erosion characterization parameter is positive, a negative sign is added to the right side of the equation. Therefore, the pressure wave power density formula is:

[0038]

[0039] In addition, according to Melissaris, the convection term on the right side of the above equation is ignored. The pressure wave power density is finally expressed as:

[0040]

[0041] Step 2.2: Calculate the instantaneous steam volume fraction using the first-order backward difference method. Multiply the calculated steam volume fraction and the average pressure field by the pressure difference at each node on the hydrofoil surface, and then add a negative sign to the multiplication result to obtain the cavitation erosion index characterized by the pressure wave power density.

[0042] The specific implementation method of Step 3 is as follows:

[0043] Step 3.1: Since the elastic material hydrofoil will undergo bending and torsional deformation due to the impact force generated by the cavity collapse, which in turn affects the intensity of the shock wave generated by the subsequent cavity collapse. Combine the shear modulus, Young's modulus, and Poisson's ratio of the elastic material to construct an erosion index correction factor F for characterizing the degree of bending and torsional deformation of the elastic material hydrofoil:

[0044]

[0045] where E is the Young's modulus of the elastic material, G is the shear modulus of the elastic material, υ is the Poisson's ratio of the elastic material, m and n are dimensionless exponents, and k is a dimensionless parameter used to adjust the magnitude of the influence of the material bending-torsion coupling effect on the material deformation.

[0046] Step 3.2: The product of the erosion index correction factor and the cavitation erosion index characterized by the pressure wave power density is the corrected cavitation erosion index at each position node.

[0047] The method for calculating the instantaneous cavitation index is as follows:

[0048] p pot修正 = F·p pot (3)

[0049] where p pot修正 is the instantaneous erosion index, F is the correction factor introduced considering the material deformation caused by the fluid-structure interaction effect, and p pot is the instantaneous pressure wave power, that is, the instantaneous erosion load.

[0050] The specific implementation method of Step 4 is as follows:

[0051] Step 4.1: Based on the fatigue strength of the material itself and the cumulative effect of cavitation occurrence, when the corrected cavitation erosion index is greater than the threshold, it is determined that the intensity of the shock wave will cause cavitation to the material on the hydrofoil surface. Based on this, screen the corrected cavitation erosion index at each position node.

[0052]

[0053] where p pot修正 is the corrected instantaneous erosion index

[0054] Step 4.2: Superimpose according to each time step. The result after division by the number of modified cavitation erosion indices greater than the threshold is the final cavitation risk index. The modified cavitation erosion index is

[0055]

[0056] E is the final cavitation risk index obtained after considering the effects of below-threshold and material cumulative load. N is the number of all instantaneous moments when the pressure wave power density p pot is greater than the selected threshold. The subscript i represents each time point.

[0057] The specific implementation method of Step 5 is as follows:

[0058] Extract the CSV table file of the point-line relationship and geometric relationship output by CFX, and then import it into TECPLOT to construct the geometric model. Interpolate the modified cavitation erosion index data into the RGB color data, and use this data as the fourth dimension to map to the geometric structure model of the elastic material hydrofoil, and characterize the magnitude of the modified cavitation erosion index value by color change.

[0059] Beneficial effects:

[0060] 1. Compared with the previous methods, a cavitation prediction method for elastic material hydrofoils based on potential energy theory disclosed in the present invention introduces a new correction factor based on potential energy theory. The introduction of this correction factor takes into account that the elastic material hydrofoil will bend and twist due to the impact force generated by the collapse of the cavity, thereby affecting the intensity of the shock wave generated by the cavity collapse. Based on this correction, the erosion range on the surface of the elastic material hydrofoil can be predicted more accurately.

[0061] 2. A cavitation prediction method for elastic material hydrofoils based on potential energy theory disclosed in the present invention uses a tightly coupled algorithm for computational fluid-structure interaction to set up a fluid-structure interaction interface, perform data exchange and iteration between the structural field and the flow field, and complete the calculation after convergence. The present invention can quickly and accurately calculate the relevant physical quantities on the surface of the hydrofoil under given working conditions, improving the efficiency of cavitation prediction for elastic material hydrofoils. Description of the Drawings

[0062] Figure 1 It is a flowchart of a fluid-structure interaction cavitation prediction method for elastic material hydrofoils based on potential energy theory of the present invention.

[0063] Figure 2 It is the final result of cavitation risk prediction for elastic material hydrofoils. Detailed Embodiments

[0064] For the convenience of those of ordinary skill in the art to understand and implement the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0065] Embodiment 1

[0066] As Figure 2 shown, this embodiment provides a method for predicting the fluid-structure interaction cavitation of an elastic material hydrofoil based on the potential energy theory, and the specific implementation steps are as follows:

[0067] Step 1: Establish a three-dimensional flow domain and hydrofoil geometric model, divide the flow domain grid, and establish a computational fluid dynamics model;

[0068] Establish a three-dimensional flow domain and hydrofoil geometric model for the given elastic material hydrofoil in the preprocessing software ICEM CFD. The hydrofoil material is POM, and the main material properties are: the elastic modulus E is 3000 MPa, the density ρ is 1480 kg / m 3 , and the Poisson's ratio is 0.35. The fluid domain is divided into two parts. The part around the hydrofoil uses unstructured grids, and the near-wall grids are encrypted. The outer domain grids use structured grids, and it is ensured that the grid sizes at the interface with the inner domain grids are the same; the basic control equations of the flow field of the computational fluid model adopt the homogeneous flow model, ignoring the relative velocity and interaction between the vapor / liquid phases. The basic control equation set includes the continuity equation and the momentum equation:

[0069]

[0070] Among them, represents the partial derivative of the function with respect to the corresponding variable, ρ is the density of the fluid, t is the time, p is the pressure at the fluid inlet,, u i , u j represent the velocity components of the fluid, μ l and μ t are the laminar and turbulent viscosity coefficients of the fluid respectively, x i , x j represent the position components of the fluid;

[0071] The structural field control equation (2) is:

[0072]

[0073] Among them, [M s , [C s , [K s are the mass matrix, damping matrix and stiffness matrix of the hydrofoil structure of the material respectively, {X} is the structural displacement, is the structural velocity, is the structural acceleration, {FCFD} represents the fluid force on the structure under the fluid-structure interaction, {F EX} represents the external excitation force on the structure under the fluid-structure interaction;

[0074] The k-ω SST turbulence model is adopted:

[0075]

[0076] where k is the turbulent kinetic energy, ω is the turbulent frequency, D k is the turbulent dissipation term, P k and P ω are the turbulent production terms, F1 and F2 are the blending functions, S is the constant term of the shear stress tensor, μ t is the turbulent viscosity coefficient.

[0077]

[0078] Step 2, perform the initial steady-state fluid field numerical calculation and the fluid-structure interaction calculation of the unsteady fluid field;

[0079] Based on ANSYS CFX, perform the numerical calculation. Taking the steady-state fluid field numerical calculation results in Step 1 as the initial conditions, then transfer the data such as pressure and velocity of the steady-state fluid field initial values to the structural field through the fluid-structure interaction interface to solve the finite element structural deformation; subsequently, transfer the information such as the structural field deformation to the unsteady fluid field through the fluid-structure interaction interface, update the fluid field grid and solve the fluid field according to the structural deformation. According to the solution results of the sub-iteration steps within each time step, judge whether it converges. If the requirements are met, directly enter the next time step calculation; if the requirements are not met, judge whether the number of sub-iteration steps is less than the maximum number of iteration steps. If the requirements are met, continue the sub-iteration convergence solution calculation. If the requirements are not met, enter the next time step calculation. Through the continuous solution of the sub-iteration steps within each time step, convergence is achieved and the calculation is completed.

[0080] Step 3, obtain the CSV table files of the instantaneous pressure and instantaneous vapor volume fraction on the surface of the elastic material hydrofoil through CFX post-processing; input the saturated vapor pressure of 3169 Pa and the set time step of 0.00001 s, and read and store the CSV table files;

[0081] Step 4, calculate the instantaneous terms using the first-order backward difference method, and then calculate the instantaneous erosion index of each node at each time interval according to the instantaneous pressure, average pressure, instantaneous vapor volume fraction, time step, and hydrofoil coordinate data;

[0082] Step 5: Query parameters such as the elastic modulus, shear modulus, and Poisson's ratio of the elastic material, substitute them into the core formula, calculate the instantaneous cavitation index according to the core formula, and superimpose the erosion indices at different times on each node after screening according to the threshold, and consider the material cumulative effect to calculate the corresponding final cavitation risk index at each node coordinate;

[0083] Step 6: Based on the point - surface structure data of the geometric model, reconstruct the geometry by sequentially connecting each node, interpolate the cavitation risk index into the RGB color data, and use this data as the fourth dimension to cover on the reconstructed model. Characterize the numerical size by the color change, and finally obtain the result as shown in Figure 2 shown, Figure 2 where the color from deep to light represents the cavitation risk from low to high. That is, in the example result, the cavitation risk is mainly concentrated at the span - wise center part of the elastic material hydrofoil, and the cavitation risk area gradually decreases from the tip to the tail.

[0084] In the above - mentioned embodiment, the potential energy expression of the cavitation cloud is as follows:

[0085] E pot =ΔP·V v

[0086] In the above formula, ΔP = P f -P v where P f is the environmental pressure outside the cloud, P v is the pressure inside the cloud, which is the saturated vapor pressure, and V v is the steam volume.

[0087] The instantaneous power is the derivative of the potential energy with respect to time. Since the change rate of the steam volume is one order of magnitude higher than the change rate of the pressure difference inside and outside the steam, the term V v {d(ΔP) / dt} is ignored. Divide both sides of the equation by the total volume of the total grid occupied by the cloud, and the instantaneous power p per unit volume in the cloud can be obtained pot . The amplitude p wave of the pressure wave is proportional to . Use p pot to simplify and replace p wave to qualitatively estimate the erosion risk area. The instantaneous erosion load, that is, the instantaneous pressure wave power density p pot expression is as follows:

[0088]

[0089] The environmental pressure field p f is the pressure field that effectively drives the cavity to collapse. However, it is extremely difficult to accurately predict this pressure field in the cavitation field and requires a large amount of computing resources. Use the average pressure field result to replace the environmental pressure field p fErosion assessment is carried out. The pressure wave power density formula is modified as follows:

[0090]

[0091] If only the contraction process during cavitation is considered, then should be negative. That is, when the rate of change of the vapor volume fraction around the vapor bubble with time is less than zero, it is considered that the cavitation on the surface of the hydrofoil is in the contraction stage, and its collapse result will cause cavitation erosion risk. To ensure that the cavitation characterization parameter is positive, a negative sign is added to the right side of the equation. Therefore, the pressure wave power density formula is:

[0092]

[0093] In addition, according to the suggestion of Melissaris, the convection term on the right side of the above formula is ignored. The pressure wave power density is finally expressed as:

[0094]

[0095] Compared with the prior art, the method provided by this application first applies the cavitation result of the elastic material hydrofoil obtained by fluid-structure interaction calculation to the cavitation erosion prediction calculation of the elastic material hydrofoil. Under a certain incoming flow velocity, the elastic material hydrofoil undergoes bending and torsional deformation, and the changes in the structural field and the flow field of the elastic material hydrofoil interact with each other. The cavitation erosion factor, as a characterization of the cavity energy, will change with the change of the cavity structure. This method describes and corrects the cavitation risk at each instantaneous moment by introducing a correction factor related to the properties of the elastic material. Considering the fluid-structure interaction, the parameter F is introduced as the correction factor, integrating numerical simulation and experimental data.

[0096] Therefore, the method for calculating the instantaneous cavitation index is as follows:

[0097] p pot修正 = F·p pot

[0098] where p pot修正 is the instantaneous erosion index, F is the correction factor introduced considering the material deformation caused by the fluid-structure coupling effect, and p pot is the instantaneous pressure wave power, that is, the instantaneous erosion load.

[0099] The expression of the final cavitation risk index is as follows:

[0100]

[0101] E is the final cavitation risk index obtained considering the effects of below-threshold and material cumulative load, N is the number of all instantaneous moments when the pressure wave power density p pot is greater than the selected threshold, and the subscript i represents each time point. After calculation, the threshold is generally selected as 3×105 。

[0102] The expression of the correction factor F is as follows:

[0103]

[0104] Among them, E is the Young's modulus of the elastic material, G is the shear modulus of the elastic material, υ is the Poisson's ratio of the elastic material, which can be obtained by looking up the table. m and n are dimensionless exponents, and k is a dimensionless parameter used to adjust the magnitude of the influence of the material bending-torsion coupling effect on the material deformation.

[0105] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A fluid-structure interaction cavitation prediction method for elastic material hydrofoils based on potential energy theory, characterized in that: It includes the following steps: Step 1: Establish a three-dimensional watershed and hydrofoil geometric model, and perform mesh division on the three-dimensional watershed and hydrofoil respectively; import the divided three-dimensional watershed and hydrofoil meshes into the System Coupling module of the Ansys Workbench platform to perform initial steady-state flow field numerical calculation and fluid-structure interaction calculation of the unsteady flow field, and obtain a CSV table file of the pressure and steam volume fraction distribution on the hydrofoil surface; Step 2: Calculate the CSV table file of the pressure and steam volume fraction distribution at each node on the hydrofoil surface at each time step. Use the first-order backward difference method to calculate the instantaneous steam volume fraction, and multiply the calculated steam volume fraction and the average pressure field by the pressure difference at each node on the hydrofoil surface. Add a negative sign to the multiplication result to obtain the cavitation erosion index characterized by the pressure wave power density; Step 3: Since the elastic material hydrofoil will undergo bending and torsional deformation due to the impact force generated by the cavity collapse, which will in turn affect the intensity of the shock wave generated by the subsequent cavity collapse. Combine the shear modulus, Young's modulus, and Poisson's ratio of the elastic material to construct an erosion index correction factor F for characterizing the degree of bending and torsional deformation of the elastic material hydrofoil. The product of the erosion index correction factor and the cavitation erosion index characterized by the pressure wave power density is the cavitation erosion index of each position node after correction; Step 4: Based on the fatigue strength of the material itself and the cumulative effect of cavitation occurrence, when the corrected cavitation erosion index is greater than the threshold, it is determined that the intensity of the shock wave will cause cavitation to the material on the hydrofoil surface. Based on this, screen the cavitation erosion index of each position node after correction, and perform superposition according to each time step. The result after superposition divided by the number of corrected cavitation erosion indices greater than the threshold is the final cavitation risk index. The corrected cavitation erosion index can more accurately predict the cavitation risk on the surface of the elastic material hydrofoil.

2. The hydrodynamic cavitation prediction method for fluid-structure interaction of an elastic material hydrofoil based on potential energy theory according to claim 1, characterized in that: It also includes Step 5: Interpolate the corrected cavitation erosion index data into RGB color data, and map this data as the fourth dimension into the geometric structure model of the elastic material hydrofoil to characterize the magnitude of the corrected cavitation erosion index value by color change, and more significantly and accurately realize the prediction of the cavitation risk area on the surface of the elastic material hydrofoil according to the color change.

3. A fluid-structure interaction cavitation prediction method for an elastic material hydrofoil based on potential energy theory according to claim 1 or 2, characterized in that: The specific implementation method of Step 1 is as follows: Step 1.1: Establish a three-dimensional watershed and hydrofoil geometric model, and perform mesh division on the three-dimensional watershed and hydrofoil respectively. The fluid domain mesh is divided into two parts. The part around the hydrofoil uses unstructured mesh, and at the same time, the near-wall mesh is encrypted. The outer domain mesh around the hydrofoil uses structured mesh to ensure that the mesh sizes at the interface with the inner domain mesh are the same; Step 1.2: Given no-slip and smooth wall boundary conditions on the elastic hydrofoil surface and the three-dimensional watershed boundary, and set the elastic material hydrofoil surface as the fluid-structure interaction interface; Step 1.3: Import the divided three-dimensional basin and hydrofoil grids into the System Coupling module of the Ansys Workbench platform to perform initial steady-state flow field numerical calculations and fluid-structure interaction calculations for the unsteady flow field. Solve the steady-state flow field initial values according to the flow field control equations shown in Equations (1.1) and (1.2). Transfer the pressure and velocity data of the steady-state flow field initial values to the structural field through the fluid-structure interaction interface. Solve the finite element structural deformation of the structural field according to Equation (2) to obtain the finite element structural deformation; The flow field control equations for the computational fluid domain adopt the homogeneous flow model. To simplify the calculation process and improve the calculation speed, the relative velocity and interaction between the vapor / liquid phases are ignored; the flow field control equation set includes the continuity equation and the momentum equation: Among them, represents the partial derivative of the function with respect to the corresponding variable, ρ is the density of the fluid, t is the time, p is the pressure at the fluid inlet, u i and u j represent the velocity components of the fluid, μ m and μ t are the laminar and turbulent viscosity coefficients of the fluid respectively, x i and x j represent the position components of the fluid; The structural field control equation (2) is: Among them, [M s , [C s , [K s are the mass matrix, damping matrix and stiffness matrix of the hydrofoil structure of the only material, respectively, {X} is the structural displacement, is the structural velocity, is the structural acceleration, {F CFD} represents the flow field force acting on the structure under fluid-structure interaction, and {F EX} represents the external excitation force acting on the structure under fluid-structure interaction; Step 1.4: Transfer information such as the structural field deformation to the unsteady flow field through the fluid-structure interaction interface. Update the flow field grid and solve the flow field according to the structural deformation to obtain the flow field solution results; Step 1.5: According to the solution results of the sub-iteration steps within each time step, judge whether it converges. If the requirements are met, directly enter the calculation of the next time step; if the requirements are not met, judge whether the number of sub-iteration steps is less than the maximum number of iteration steps. If the requirements are met, continue the sub-iteration convergence solution calculation. If the requirements are not met, enter the calculation of the next time step Step 1.6: After continuous solution of the sub-iteration steps within each time step, when the calculation converges, the fluid-structure interaction calculation is completed, and a CSV table file of the pressure and steam volume fraction distributions on the hydrofoil surface is output.

4. A fluid-structure interaction cavitation prediction method for an elastic material hydrofoil based on potential energy theory according to claim 3, characterized in that: The specific implementation method of Step 2 is as follows: Step 2.1: The cavitation erosion index characterized by the pressure wave power density is the result of derivation based on potential energy theory. The potential energy expression of the cavitation cloud is as follows: E pot = ΔP·V v In the above formula, ΔP = P f - P v , where P f is the environmental pressure outside the cloud mass, and P v is the pressure inside the cloud mass, which is the saturated vapor pressure, and V v is the steam volume; The instantaneous power is the derivative of the potential energy with respect to time. Since the rate of change of the vapor volume is one order of magnitude higher than the rate of change of the pressure difference inside and outside the vapor, the term V v {d(ΔP) / dt} is ignored; the total volume V of the total number of grids occupied by the cloud is divided on both sides of the equation cell , and the instantaneous power p per unit volume in the cloud is obtained pot ; the amplitude p of the pressure wave wave is proportional to ; p pot is simplified and replaced with p wave to qualitatively estimate the erosion risk area; α v is the vapor volume fraction, and the instantaneous erosion load is the instantaneous pressure wave power density p pot The expression is as follows: Ambient pressure field p f is the pressure field that effectively drives the collapse of the cavity; however, it is extremely difficult to accurately predict this pressure field in the cavitation field and requires a large amount of computing resources; the average pressure field result is used to replace the ambient pressure field p f for erosion assessment; the pressure wave power density formula is modified as follows: If only the contraction process during cavitation is considered, then it should be negative; that is, when the rate of change of the vapor volume fraction around the vapor bubble with time is less than zero, it is determined that the surface cavity of the hydrofoil is in the contraction stage, and its collapse result will cause cavitation risk; to ensure that the cavitation characterization parameter is positive, a negative sign is added to the right side of the equation; therefore, the pressure wave power density formula is: In addition, according to Melissaris, the convective term on the right side of the above formula is ignored; the pressure wave power density is finally expressed as: Step 2.2: Use the first-order backward difference method to calculate the instantaneous steam volume fraction. Multiply the calculated steam volume fraction and the pressure difference at each node on the hydrofoil surface of the average pressure field, and add a negative sign to the multiplication result to obtain the cavitation erosion index characterized by the pressure wave power density.

5. A fluid-structure interaction cavitation prediction method for elastic material hydrofoils based on potential energy theory according to claim 4, characterized in that: The specific implementation method of Step 3 is as follows: Step 3.1: Since the elastic material hydrofoil will undergo bending and torsional deformation due to the impact force generated by the cavity collapse, which will in turn affect the intensity of the shock wave generated by the subsequent cavity collapse. Combine the shear modulus, Young's modulus, and Poisson's ratio of the elastic material to construct an erosion index correction factor F for characterizing the degree of bending and torsional deformation of the elastic material hydrofoil: Among them, E is the Young's modulus of the elastic material, G is the shear modulus of the elastic material, υ is the Poisson's ratio of the elastic material, m and n are dimensionless exponents, and k is a dimensionless parameter used to adjust the magnitude of the influence of the material bending-torsion coupling effect on the material deformation; Step 3.2: The product of the erosion index correction factor and the cavitation erosion index characterized by the pressure wave power density is the cavitation erosion index of each position node after correction; The method for calculating the instantaneous cavitation index is as follows: p pot修正 = F·p pot (3) Among them, p pot修正 is the instantaneous erosion index, F is the correction factor introduced considering the material deformation caused by the fluid-structure coupling effect, and p pot is the instantaneous pressure wave power, that is, the instantaneous erosion load.

6. A fluid-structure interaction cavitation prediction method for elastic material hydrofoils based on potential energy theory according to claim 5, characterized in that: The specific implementation method of Step 4 is as follows: Step 4.1: Based on the fatigue strength of the material itself and the cumulative effect of cavitation occurrence, when the corrected cavitation erosion index is greater than the threshold value, it is determined that the intensity of this shock wave will cause cavitation to the material on the hydrofoil surface. Based on this, the cavitation erosion index of each position node after correction is screened. where p pot修正 is the corrected instantaneous erosion index Step 4.2: Superimpose according to each time step. The result after superimposition divided by the number of corrected cavitation erosion indices greater than the threshold value is the final cavitation risk index. The corrected cavitation erosion index is E is the final cavitation risk index obtained after considering the effects of below-threshold and material cumulative load, and N is the number of all instantaneous moments when the pressure wave power density p pot is greater than the selected threshold, and the subscript i represents each time point.

7. A fluid-structure interaction cavitation prediction method for elastic material hydrofoils based on potential energy theory according to claim 6, characterized in that: The specific implementation method of Step 5 is as follows: By extracting the CSV table file of the point-line relationship and geometric relationship output by CFX, and then importing it into TECPLOT to construct the geometric model; then interpolate the corrected cavitation erosion index data into the RGB color data, and use this data as the fourth dimension to map into the geometric structure model of the elastic material hydrofoil, and represent the magnitude of the corrected cavitation erosion index value by color change.

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