Method for simulating dynamic material erosion process based on porosity change

Abstract

The application discloses a method for simulating a dynamic damage process of material cavitation erosion based on porosity change. The method comprises the following steps: importing a calculation domain grid of a material to be measured into a modeling software, configuring a water-vapor multiphase flow model, a turbulent flow model and boundary conditions; marking a layer of thin grid area on the surface of the calculation domain grid of the material to be measured as a damage layer, and cutting the calculation domain through domain segmentation; determining a cavitation model; standardizing initialization and setting the initial porosity of the damage layer as 0; constructing a porous medium flow control model; introducing the porous medium flow control model to the damage layer, and utilizing a user-defined function to dynamically correlate the porosity with a local pressure value; performing calculation and drawing a cloud picture of the porosity of the material to be measured. The application directly represents the cavitation erosion damage process through the porosity change, and can obtain a cavitation erosion damage evolution process which is more in line with the physical reality. Meanwhile, the application provides a new idea for evaluating the cavitation damage mechanism and studying the application of cavitation in actual engineering through the numerical simulation method.

Description

Technical Field

[0001] This invention belongs to the technical fields of engineering computational fluid dynamics and computer-aided design, and in particular relates to a method for simulating the dynamic failure process of material cavitation by using a porous medium model to simulate the change of porosity. Background Technology

[0002] Cavitation is a complex phenomenon prevalent in engineering fluid mechanics, commonly found in hydraulic machinery (such as turbines and pumps), ship propulsion systems, valves, and other equipment. When the local pressure drops below the saturated vapor pressure of a liquid, vapor-filled cavitation bubbles form inside the liquid. These bubbles, carried by the flow field to high-pressure regions, rapidly collapse, generating instantaneous high temperatures, high pressures, and microjets. The impact force generated by the repeated collapse of these bubbles acts on the solid wall, leading to material fatigue erosion, or cavitation failure. Accurately simulating the dynamic evolution of cavitation failure is crucial for predicting equipment lifespan and optimizing design. Traditional simulation methods mainly rely on complex fluid-structure interaction (FSI) models, which incur a huge computational burden and typically only predict the final failure mode or the stress state at a specific moment, making it difficult to intuitively and efficiently demonstrate the dynamic expansion process of cavitation failure over time.

[0003] Furthermore, a significant vicious cycle exists between cavitation and erosion: cavitation is more likely to occur in areas where cavitation has already occurred (material is eroded to form micro-pits) because these small pits on the material surface significantly alter the local flow state, triggering flow separation and low-pressure areas, thus exacerbating cavitation; and this exacerbated cavitation further accelerates the erosion and damage of the local material, forming a self-reinforcing cycle of deterioration. Traditional simulation methods cannot reflect the dynamic changes in material failure, and therefore cannot capture or represent this crucial deterioration mechanism.

[0004] Therefore, there is an urgent need to develop a new method that can intuitively and efficiently simulate the dynamic process of cavitation damage and reflect the vicious cycle mechanism of cavitation-cavitation. Summary of the Invention

[0005] To address the aforementioned technical problems, this application provides a method that can intuitively and efficiently simulate the dynamic evolution of cavitation erosion damage. This method utilizes the change in porosity in a porous media model to characterize the degree of material damage, overcoming the shortcomings of traditional fluid-structure interaction models, such as high computational burden and difficulty in representing dynamic damage processes. Furthermore, by simulating the dynamic changes in material damage, it can indirectly reflect the vicious cycle mechanism of cavitation erosion exacerbating local cavitation.

[0006] The technical solution provided in this application is as follows.

[0007] Methods for simulating the dynamic cavitation failure process of materials based on porosity changes include: Import the computational domain mesh of the material to be tested into the modeling software, and configure the water-vapor multiphase flow model, turbulence model and boundary conditions; A thin mesh region is marked on the surface of the computational domain mesh of the material under test as a damage layer, and the computational domain is cut by domain segmentation. Determine the cavitation model; Standard initialization and setting the initial porosity of the damaged layer to 0; A porous media flow control model is constructed; the porous media flow control model is used to simulate cavitation erosion damage by utilizing the change in porosity of the material under test. A porous media flow control model is introduced into the damaged layer, and a user-defined function is used to dynamically correlate porosity with local pressure values. Perform calculations and plot a contour map of the porosity of the material to be tested.

[0008] In one possible implementation, the water-vapor multiphase flow model has liquid water as the primary phase and water vapor as the secondary phase.

[0009] In one possible implementation, the boundary conditions include the boundary surface, velocity inlet, turbulence intensity, hydraulic diameter, liquid water volume fraction, and pressure outlet static pressure.

[0010] In one possible implementation, the cavitation model is:

[0011] In the formula, ν Let α be the vapor phase, and α be the vapor phase volume fraction. Represents the vector differential operator. For vapor density, For vapor phase velocity, , These are the mass transfer source terms related to the growth and collapse of steam bubbles in cavitation.

[0012] Furthermore, in the cavitation model, When evaporating, :

[0013] When it solidifies :

[0014] in, and These are the empirical calibration coefficients for evaporation and condensation, respectively. ρ l The density of the liquid phase is... ρ For the density of the mixture, Where is the bubble radius. PFor local far-field pressure, This refers to the steam pressure.

[0015] In one possible implementation, the method for constructing a porous media model includes: introducing mass source terms and momentum source terms into the standard fluid flow control equations to obtain the porous media flow control equations.

[0016] Furthermore, the flow control equations for the porous media include a continuity equation, a momentum equation, and an energy equation; The formula for the continuity equation is:

[0017] The formula for the momentum equation is:

[0018] The formula for the energy equation is:

[0019] In the above three formulas: t is time, γ is porosity, and α is... q It is the volume fraction of phase q, ρ q It is the density of the q phase. d is the velocity vector of phase q, q and d are phase labels used to distinguish different fluid phases, and n is the total number of phases in the system. and These are the mass transfer rates from phase d to phase q and from phase q to phase d, respectively; S q It is the mass source term of phase q; p is the liquid pressure, p c It is the capillary pressure of the wetting phase. It is the shear stress tensor of phase q. It is a volume force. μ q S is the dynamic viscosity coefficient of phase q. i It is a momentum source term. It is the drag force in the non-porous flow / region. It is turbulent dispersion force. It is the velocity vector of phase d relative to phase q. It is the velocity vector of phase q relative to phase d; , , These represent the external volume force, lift force, and virtual mass force acting on the q phase, respectively; s represents the solid material; h q It is the enthalpy of phase q, h s It is the enthalpy of the solid phase; k is the thermal conductivity, k q It is the thermal conductivity of the q phase, k s It is the thermal conductivity of a solid material; p q It is the pressure of phase q, Q dqIt is the heat transfer between phase d and phase q, ρ is the density, and T is the heat transfer between phases d and q. q It is the temperature of phase q. For the energy source term, h dq and h qd These are the enthalpy differences corresponding to mass transfer from phase d to phase q and from phase q to phase d, respectively.

[0020] Furthermore, the formula for the momentum source term is:

[0021] In the formula, S i It is the first i The source term of the momentum equation, i = x, y, or z; K is the absolute penetration rate, K r,q C1 is the relative permeability of phase q, and C2 is the inertial drag factor.

[0022] In one possible implementation, the method of dynamically associating porosity with local mixed-phase pressure values ​​using a user-defined function includes: Obtain the porosity γ at the current time step current and the largest historical gamma histmax ; At each time step, the fault layer mesh cells are traversed according to the local mixed phase pressure value C. P Determine the porosity at the current time step; if C P If the stress is greater than the yield stress of the material being tested, then let γ be... new = 1.0, indicating the formation of cavitation pits; otherwise γ new = 0.0 indicates that the material is intact, that is

[0023] In the formula, C P (i,t) represents the local mixed-phase pressure of element i at time t, σ y γ is the yield stress of the material. new (i,t) represents the new porosity state calculated based on the current pressure; Set the γ of the current unit current The value is set to γ new Compared with the historical maximum value γ histmax The larger one in the middle, and update γ. histmax ,Right now: ; Calculate the γ of the current unit current The value is assigned to the porosity variable.

[0024] In one possible implementation, the cloud map shows the destructive process and destruction area of ​​cavitation on the simulated material through the spatial distribution change of porosity from undisturbed to completely destroyed.

[0025] The beneficial effects of this application are as follows: 1. Intuitive and efficient simulation of dynamic damage: By showing the change of porosity from 0 to 1, the dynamic expansion process of cavitation damage over time and space is presented intuitively and clearly, overcoming the shortcomings of traditional fluid-structure interaction models, which have a large computational burden and cannot intuitively reflect the dynamic process.

[0026] 2. Reflecting the vicious cycle mechanism: By simulating material failure through irreversible increase in porosity, this method can indirectly reflect the impact of cavitation damage on local flow, forming pits and changing the flow field. It can then simulate the key vicious cycle mechanism that cavitation damage areas are more likely to induce and exacerbate cavitation, and the exacerbated cavitation further accelerates material failure in these areas. This is something that traditional methods cannot achieve.

[0027] 3. More reasonable physical basis: The destruction process is dynamically linked to the local fluid pressure (the direct driving force of cavitation), and the cumulative effect of material destruction is simulated through irreversible constraints, making the simulated cavitation destruction evolution process more in line with physical reality.

[0028] 4. Provides new research ideas: It provides a new and efficient technical approach for in-depth evaluation of cavitation damage mechanism, prediction of damage area, optimization of equipment anti-cavitation design, and research on the application of cavitation in related engineering (such as cavitation cleaning and cavitation degradation) through numerical simulation. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the implementation of the simulation of cavitation-induced damage using a porous media model with variations in porosity.

[0030] Figure 2 The diagram and specific geometric parameters of the ALE15 hydrofoil model are provided. Figure 2 (a) is a model diagram of the ALE15 hydrofoil. Figure 2 (b) are the specific geometric parameters of the hydrofoil model.

[0031] Figure 3 The computational domain and related boundary conditions are given for the ALE15 hydrofoil failure example.

[0032] Figure 4 The computational domain mesh structure is shown for the ALE15 hydrofoil failure example.

[0033] Figure 5 Porosity contour plots at different times in the ALE15 hydrofoil failure case study. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be fully described below in conjunction with the relevant accompanying drawings. In particular, the described embodiments are not all embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0035] In the description of this invention, the indicated orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and are not intended to indicate or imply that the described device or element must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0036] See Figure 1 This application provides a method for simulating the dynamic failure process of material cavitation based on porosity changes, including: S101. Import the computational domain mesh of the material to be tested into the modeling software, and configure the water-vapor multiphase flow model, turbulence model and boundary conditions.

[0037] In one possible implementation, the modeling software includes Ansys Fluent.

[0038] In one possible implementation, the water-vapor multiphase flow model includes a Mixture multiphase flow model, specifying the primary phase as water-liquid and the secondary phase as water-vapor; the turbulence model includes a conventional turbulence model, such as a Realizable k-ε model, with Enhanced Wall Treatment enabled.

[0039] In one possible implementation, the boundary conditions include: boundary surface, velocity inlet, turbulence intensity, hydraulic diameter, liquid water volume fraction, and pressure outlet static pressure.

[0040] S102. Mark a thin mesh region on the surface of the computational domain mesh of the material to be tested as a damage layer, and cut the computational domain by domain segmentation.

[0041] Understandably, the collapse of cavitation-induced bubbles can create extremely high pressure in a localized area, leading to cavitation erosion and changes in the local porosity of the material. Marking the damaged layer is used to visually and clearly demonstrate the cavitation erosion process and its extent.

[0042] S103. Determine the cavitation model.

[0043] In one possible implementation, the cavitation model is: (1) In the formula, ν Let α be the vapor phase, and α be the vapor phase volume fraction. Represents the vector differential operator. For vapor density, For vapor phase velocity, , These are the mass transfer source terms related to the growth and collapse of steam bubbles in cavitation.

[0044] Furthermore, when evaporating, : (2) When it solidifies : (3) in, and These are the empirical calibration coefficients for evaporation and condensation, respectively. The density of the liquid phase is... ρ For the density of the mixture, Where is the bubble radius. P For local far-field pressure, This refers to the steam pressure.

[0045] It should be noted that the explanation and derivation process of the cavitation model are as follows.

[0046] In a flowing liquid, when the pressure in a local area suddenly drops below the vapor pressure corresponding to the liquid temperature in that area, part of the liquid vaporizes, and the gas dissolved in the liquid escapes, forming bubbles in the liquid flow. This process is called cavitation. When cavitation bubbles enter a region of higher pressure with the liquid flow, they lose the conditions for existence and suddenly collapse. The movement of the liquid around the original cavitation bubbles causes a sudden increase in pressure in the local area. If cavitation bubbles that continuously form and grow in the liquid flow frequently collapse near solid walls, the walls will be subjected to repeated impacts of enormous pressure, leading to fatigue damage or even surface erosion of the material, resulting in cavitation erosion.

[0047] The standard two-phase cavitation model makes the following assumptions: the simulated system must contain both a liquid and a vapor phase; mass transfer between the liquid and vapor phases is assumed. The cavitation model considers both bubble formation (evaporation) and collapse (condensation); Ansys Fluent defines mass transfer from liquid to vapor as positive for the cavitation model; the cavitation model is based on the Rayleigh-Plesset equation, which describes the growth of a single vapor bubble in a liquid; the input material properties used in the cavitation model can be constants, functions of temperature, or user-defined.

[0048] When using multiphase cavitation modeling methods, a basic two-phase cavitation model includes: a standard viscous flow equation for controlling the transport of the mixture (mixing model) or the transport of each phase (Eulerian multiphase flow), and a conventional turbulence model (such as the k-ε model).

[0049] During cavitation, liquid-vapor mass transfer (evaporation and condensation) is controlled by the steam transport equation: (4) In the formula, t represents time. Let α be the vapor phase, and α be the vapor phase volume fraction. For vapor density, R is the vapor phase velocity. e R c These are the mass transfer source terms related to steam bubble growth and collapse, respectively. In equation (4), the term R... e and R c These terms describe the mass transfer between the liquid and vapor phases during cavitation. In Ansys Fluent, these terms are modeled based on the Rayleigh-Plesset equations, which describe the growth of a single vapor bubble in a liquid.

[0050] In most engineering scenarios, the embodiments of this application assume the existence of sufficient nucleation points for cavitation initiation. Therefore, the main focus of the embodiments of this application is on the proper description of bubble growth and collapse. In flowing liquids with no velocity slip between the fluid and the bubble, the bubble dynamics equations can be derived from the generalized Rayleigh-Plesset equations: (5) In the formula, D / Dt represents the mass derivative (volume derivative), which describes the rate of change when following the motion of a fluid element. Where is the bubble radius. for The derivative, The surface tension coefficient of the liquid. For the density of the liquid, The kinematic viscosity of the liquid. Let P be the surface pressure of the bubble and P be the local far-field pressure. After neglecting the second-order terms and surface tension terms, equation (5) simplifies to: (6) This equation provides a physical method for incorporating bubble dynamics into cavitation models. It can also be viewed as a void propagation equation, and consequently, an equation for the density of the mixture.

[0051] To derive the expression for the net phase transition rate, Schnerr and Sauer used the following two-phase continuity equation: Liquid phase: (7) In the formula, R is the net phase change rate, which refers to the mass of liquid phase changing into vapor phase per unit volume per unit time; This represents the velocity of the mixed phase, specifically the combined velocity of the liquid and vapor phases.

[0052] Vapor phase: (8) mixture: (9) in: l It is a liquid phase. The density of the mixture (a function of phase volume fraction and density), the density of the mixture Defined as: (10) Solving equations (7), (8), and (9) simultaneously, we obtain the relationship between the mixture density and the vapor volume fraction (α): (11) Vapor volume fraction can be correlated with bubble number density and bubble radius: (12) Using equation (6), and combining equations (7), (8), (11) and (12), we finally obtain the expression for the net phase change rate R: (13) (14) Where R is the net phase change rate. Where is the bubble radius.

[0053] The final form of the model is as follows: when (During evaporation): (15) when (During condensation): (16) in, and These are the empirical calibration coefficients for evaporation and condensation, respectively, with default values ​​of 1 and 0.2.

[0054] S104. Standard initialization and setting the initial porosity of the damaged layer to 0.

[0055] In one possible implementation, standard initialization is the recommended initialization method for porous media simulations.

[0056] S105. Construct a porous media model; the porous media model is used to simulate cavitation damage by utilizing the change in porosity of the material under test.

[0057] In one possible implementation, the control equations for the porous media flow include a continuity equation, a momentum equation, and an energy equation. The continuity equation is expressed as follows: (17) The expression for the momentum equation is as follows: (18) in,

[0058] The energy equation is expressed as follows: (19) In the above three formulas: t is time, γ is porosity, and α is... q It is the volume fraction of phase q, ρ q It is the density of the q phase. d is the velocity vector of phase q, q and d are phase labels used to distinguish different fluid phases, and n is the total number of phases in the system. and These are the mass transfer rates from phase d to phase q and from phase q to phase d, respectively; S q It is the mass source term of phase q; p is the liquid pressure, p c It is the capillary pressure of the wetting phase. It is the shear stress tensor of phase q. It is a volume force. μ q S is the dynamic viscosity coefficient of phase q. i It is a momentum source term. It is the drag force in the non-porous flow / region. It is turbulent dispersion force. It is the velocity vector of phase d relative to phase q. It is the velocity vector of phase q relative to phase d; , , These represent the external volume force, lift force, and virtual mass force acting on the q phase, respectively; s represents the solid material; h q It is the enthalpy of phase q, h s It is the enthalpy of the solid phase; k is the thermal conductivity, k q It is the thermal conductivity of the q phase, k s It is the thermal conductivity of a solid material; pq It is the pressure of phase q, Q dq It is the heat transfer between phase d and phase q, ρ is the density, and T is the heat transfer between phases d and q. q It is the temperature of phase q. For the energy source term, h dq and h qd These are the enthalpy differences corresponding to mass transfer from phase d to phase q and from phase q to phase d, respectively. In the momentum source term formula, S i It is the first i The source term of the momentum equation, i = x, y, or z; K is the absolute penetration rate, K r,q C1 is the relative permeability of phase q, and C2 is the inertial drag factor. Absolute permeability is a physical quantity that describes the inherent, intrinsic ability of porous media (such as rocks, soils, sponges, filter cartridges, etc.) to allow single-phase fluids to pass through their interconnected pores; it is an inherent characteristic of porous media.

[0059] Furthermore, the momentum source term S i It consists of two parts: the viscous loss term (Darcy coefficient, i.e., the first term on the right side of equation (20)) and the inertial loss term (the second term on the right side of equation (20), as follows: (20) In the formula, S i It is the source term of the i-th (x-axis, y-axis, or z-axis) momentum equation; |v| is the magnitude of the velocity; D and C are predefined matrices. D ij The components representing the viscous drag coefficient tensor describe the momentum loss due to fluid viscosity. C ij The component representing the inertial drag coefficient tensor describes the momentum loss caused by fluid inertia (kinetic energy). μ Indicates the dynamic viscosity coefficient; v j These are the velocity components in the x, y, and z directions. This momentum sink acts on the pressure gradient within the porous mesh cell, producing a pressure drop proportional to the fluid velocity (or the square of the velocity) within that mesh cell.

[0060] The forces in a simple, homogeneous, porous medium are defined in equation (21). The viscous drag coefficient and the inertial drag coefficient will determine the properties of the momentum sink, and thus these forces.

[0061] To recreate the case of a simple, homogeneous, porous medium, the momentum source term S in the embodiments of this application... i Equation (21) is used to represent: (twenty one) Where i is x, y, or z, μ is the dynamic viscosity coefficient, α is the permeability, and C2 is the inertial drag factor. Simply specify D and C as diagonal matrices, with diagonal elements of 1 / α and C2 respectively (the remaining off-diagonal elements are zero).

[0062] Optionally, Ansys Fluent also allows source terms to be modeled as power-law forms of velocity magnitudes: (twenty two) C0 and C1 are user-defined empirical coefficients.

[0063] In laminar flow through a porous medium, the pressure drop is usually proportional to the velocity, and the constant C2 in formula (21) can be set to zero. Ignoring convection acceleration and diffusion effects, the porous medium model simplifies to Darcy's Law: (twenty three) Ansys Fluent calculated the pressure drops in the three (x, y, z) coordinate directions within the porous region as follows: (twenty four) Where: 1 / α ij These are elements of matrix D in equation (5), where i = x, y, z. j These are the velocity components in the x, y, and z directions. Δn x ,Δn y ,Δn z This refers to the thickness of the medium in the x, y, z directions. Here, the thickness of the medium (Δn) x ,Δn y ,Δn z α refers to the actual physical thickness of the porous region in the model. Therefore, if the thickness used in the model differs from the actual thickness, it must be adjusted in the input parameter 1 / α. ij Adjustments will be made accordingly as needed.

[0064] Ansys Fluent calculates apparent velocity based on volumetric flow rate by default. The apparent velocity in the governing equations can be expressed as: (25) Where γ is the porosity of the medium, defined as the ratio of the volume occupied by the fluid to the total volume. It is the apparent speed. It is the actual physical speed.

[0065] Ansys Fluent uses the Physical Velocity Porous Formulation to simulate multiphase flow in porous media. This formula is used to solve for the true or physical velocity field of the entire flow field, including both porous and non-porous regions. In this method, it is assumed that a universal scalar exists in the q-th phase. q represents any scalar field to be solved in this phase, and its governing equations in isotropic porous media are as follows: (26) In the formula: γ is porosity, which may vary with time and space; ρ q It is the density of the phase; α q It is the volume fraction of the phase. It is the velocity vector of the phase; Γq is the source term; Γq is the diffusion coefficient.

[0066] Assuming the porosity is isotropic and the flow is multiphase, the aforementioned continuity equation, momentum equation, and energy equation (the governing equations describing the q-th phase) are derived.

[0067] S106. Introduce a porous media model into the damaged layer and use a user-defined function to dynamically correlate the porosity with the local pressure value.

[0068] In one possible implementation, a method for introducing a porous media model into the damaged layer includes: The potential cavitation damage region in the material is defined as the porous medium region. By using the porous medium model to set the porosity, the material damage process is characterized as a dynamic change process of porosity from 0 to 1.

[0069] In one possible implementation, the method of dynamically associating porosity with local mixed-phase pressure values ​​using a user-defined function includes: Obtain the porosity γ at the current time step current and the largest historical gamma histmax ; At each time step, the fault layer mesh cells are traversed according to the local mixed phase pressure value C. P Determine the porosity at the current time step; if C PIf the stress is greater than the yield stress of the material being tested, then let γ be... new = 1.0, indicating the formation of cavitation pits; otherwise γ new = 0.0 indicates that the material is intact, that is (30) In the formula, C P (i,t) represents the local mixed-phase pressure of element i at time t, σ y γ is the yield stress of the material. new (i,t) represents the new porosity state calculated based on the current pressure.

[0070] Set the γ of the current unit current The value is set to γ new Compared with the historical maximum value γ histmax The larger one in the middle, and update γ. histmax ,Right now: (31) Calculate the γ of the current unit current The value is assigned to the porosity variable.

[0071] S107. Perform the calculation and plot the porosity contour map of the material to be tested.

[0072] The following description, in conjunction with more detailed embodiments, provides further details.

[0073] like Figure 2 The image shown is a model diagram and geometric parameters of the ALE15 hydrofoil. The ALE15 hydrofoil is 50 mm wide, 16 mm thick, and has a chord length of... C =107.9 mm, angle of attack is 5 Constructing a computing domain, such as Figure 3 As shown, the hydrofoil is fixed at a distance of 50 mm from both the upper and lower walls. The computational domain width and height are consistent with the experiment, with a length of 10 mm. C The distance between the hydrofoil head and the inlet is 3 C The tail of the hydrofoil is 6 meters from the exit. C Regarding the computational domain boundary conditions, the upper and lower walls were set as free-slip surfaces. The hydrofoil surface and the front and rear walls of the test section were set to no-slip conditions. The inlet velocity was 13 m / s, and the outlet static pressure was 196330 Pa to ensure the cavitation number. Reference experimental conditions: The density of the liquid medium is... =998.2 kg / m3, kinematic viscosity is =1×10⁻³ Pa s, surface tension =0.0717 N / m. The saturated vapor density and kinematic viscosity are respectively... =0.554 kg / m3 and =1.34×10⁻⁵ Pa s, saturated vapor pressure =2338.6 Pa. Considering the structural characteristics of the airfoil, a C-type mesh was chosen to discretize the computational domain, resulting in the following... Figure 4 The presented mesh has 3,478,800 nodes, at the hydrofoil surface. The value satisfies the constraint of being less than 1. For this example, the method described above for simulating cavitation-induced damage using changes in porosity in a porous media model can be implemented as follows.

[0074] Step 1: Grid Import and Basic Settings.

[0075] Import the computational domain mesh containing the ALE15 aluminum hydrofoil into Ansys Fluent software. Set the solver type to Transient and disable the energy equation to ignore the effect of temperature. Select the Mixture multiphase flow model, specifying the primary phase as water-liquid and the secondary phase as water-vapor. Use the Realizable k-ε turbulence model and enable Enhanced Wall Treatment. Set the density of the water-liquid to 1000 kg / m³. 3 Viscosity is 0.001 kg / m The density of water vapor, calculated according to the ideal gas law, is 0.02558 kg / m³. 3 (Corresponding to a saturated vapor pressure of 3169 Pa and a temperature of 298 K), viscosity is set to 1.34 e. -5 kg / m·s. Boundary conditions were configured as follows: Velocity Inlet: velocity set at 10 m / s, turbulence intensity at 5%, hydraulic diameter at 0.07 m, and liquid water volume fraction at 1.0; Pressure Outlet: static pressure set at 101325 Pa, and liquid water volume fraction in the recirculation at 1.0; All walls, including the aluminum hydrofoil surface and the far-field wall, were set as non-slip walls.

[0076] Step 2: Define and segment the damaged layer region.

[0077] A thin mesh region is created on the surface of the aluminum hydrofoil as a "destruction layer" to simulate the surface damage zone of the aluminum material under cavitation erosion. Its porosity variation will be used to quantify the degree of damage to the aluminum. Specifically, navigate to Solution → Cell Registers → New → Boundary..., select the aluminum hydrofoil surface boundary in the Boundary Register Dialog Box, set Cell Distance to 80 to select the 80 mesh cells closest to this boundary, preview and confirm the selected cells, then click Store to save it as a cell register (e.g., named al_destruction_layer). Next, navigate to Setting Up Domain > Separate > Cells, select the al_destruction_layer register in the Cell Registers tab of the Region Adaptation panel, click Mark to mark these cells, and then click Separate to divide the marked cells into a new independent computational domain (Cell Zone), named al_destruction_layer.

[0078] Step 3: Set up the cavitation model.

[0079] In the Mixture multiphase flow model settings, activate the cavitation option and select the Schnerr-Sauer cavitation model, based on the aforementioned method. , The formula was adjusted. Key model parameters were set as follows: saturation pressure was 3169 Pa, and nucleation site density was empirically set to 1e+11. This ensured that the phase transition process calculated by the cavitation model would act on the entire computational domain, including the al_destruction_layer region on the aluminum substrate.

[0080] Step 4: Standard initialization.

[0081] After completing the model setup, perform standard initialization (Hybrid Initialization). A key step is to use the Solution Initialization > Patch tool to perform special initialization on the aluminum damage layer region: In the Variable dropdown menu, select User Defined Memory..., then select User Memory Index 0 (corresponding to the current porosity γ_current) and User Memory Index 1 (corresponding to the historical maximum porosity γ_histmax). In Zones to Patch, select al_destruction_layer, set the Value of both to 0, and click Patch. This ensures that the porosity γ of all elements in the aluminum damage layer is 0 at the start of the simulation, meaning the simulated aluminum material is initially dense and undamaged.

[0082] Step 5: Activate the porous media model in the aluminum fracture layer and set the dynamic irreversible porosity UDF.

[0083] In Cell Zone Conditions, select the al_destruction_layer region and activate the PorousZone option. Associate the porous medium material properties with aluminum and configure the aforementioned porous medium model. In the Porous Zone settings panel, set the ViscousResistance (1 / α) of Direction 1 (x), Direction 2 (y), and Direction 3 (z) to a very high 1e. 15 kg / m 3 s, and set Inertial Resistance (C2) to 0 to ignore the inertial loss term.

[0084] Select UDF from the Porosity drop-down menu, and write, compile, and load a user-defined function (UDF) named al_dynamic_porosity.

[0085] The execution method of this UDF includes: firstly, using two user-defined memories (UDM 0 and UDM 1) to store the porosity γ of the current time step. current and the largest historical gamma histmax (Cumulative damage level); secondly, at each time step, the aluminum damage layer mesh cells are traversed, based on the local mixed phase pressure value (C). P Judgment: If C P≥241MPa (the yield stress of aluminum alloy is 241MPa; exceeding this pressure indicates that the aluminum alloy hydrofoil will be damaged by cavitation impact pressure and form cavitation pits), then let γ new = 1.0 (complete destruction of aluminum material, forming cavitation pits); otherwise γ new = 0.0 (aluminum material intact); then enforce the irreversible constraint, that is, the γ of the current element is set to 0.0. current The value is set to γ new Compared with the historical maximum value γ histmax The larger one in the middle, and update γ. histmax Finally, the current γ will be calculated. current The value is assigned to the porosity variable and stored in UDF 0 for post-processing. After compiling and loading this UDF, select to mount al_dynamic_porosity in the Porosity setting of al_destruction_layer.

[0086] Step Six: Calculation and Post-processing.

[0087] Set the time step to 1e -4 Set the total number of calculation steps (e.g., 1000 steps, corresponding to 0.1 s physical time, or extend the time based on observed stable aluminum failure patterns), and enable automatic saving (e.g., save the data file every 50 steps). Start transient calculation. After or during the calculation, perform post-processing to visualize the aluminum failure process: Load the data file for the required time steps, navigate to Results > Graphics and Animations > Contours > SetUp..., select User Defined... then Memory... in the Contours of drop-down menu, and enter 0 in User MemoryLocations (corresponding to storage γ). current In the UDM 0 configuration, select the al_destruction_layer or the aluminum hydrofoil surface as the display surface, set the level range (Min=0, Max=1), and click Display to generate a porosity γ distribution cloud map characterizing the degree of damage to the aluminum substrate. In the map, γ = 0 (blue) indicates that the aluminum material is intact, and γ = 1 (red) indicates that the aluminum material is completely destroyed (cavitation pits). By creating an animation sequence, the dynamic evolution of γ from 0 to 1 over time can be visually displayed, clearly reflecting the starting position, expansion area, deepening degree, and final morphology of cavitation damage on the aluminum hydrofoil surface.

[0088] All calculation steps in the method described in this application are completed in the commercial software Ansys Fluent. The calculation process and parameter settings are controlled by Fluent text commands to achieve a fully automated simulation process.

[0089] This embodiment uses the finite volume method to discretize the governing equations. The computational domain is spatially discretized using a high-quality C-type structured hexahedral mesh, with a total mesh count of approximately 2.54 million. Turbulence calculations employ the Realizable k-ε model, the Mixture model is used for multiphase flow, and the Schnerr-Sauer cavitation model is used to simulate the cavitation process. Boundary conditions are set as a velocity inlet (10 m / s) and a pressure outlet (101325 Pa), with no-slip boundary conditions applied to the computational domain walls. Pressure-velocity coupling is achieved using the SIMPLE algorithm with a time step of 10. -4 The porous media model and fluid calculations are bidirectionally coupled, using dynamic porosity changes to reflect the impact of aluminum material failure on the flow field in real time. For example... Figure 5 As shown, the method provided in this application successfully captured the formation and evolution process of cavitation clouds on the surface of an aluminum hydrofoil. The cavitation cloud formation stage involves frequent vapor-liquid phase transitions at the hydrofoil's leading edge, inducing large-scale, relatively shallow cavitation pits. The cavitation cloud shedding stage involves the instantaneous collapse of U-shaped and tornado-shaped cavities in the high-pressure region, resulting in relatively deep cavitation pits concentrated in the middle of the hydrofoil. Cavitation is mainly concentrated in the low-pressure area behind the suction peak on the upper surface. Figure 5 (b) The porosity distribution of the damaged layer shows that the damaged area of ​​the aluminum material (γ=1) is highly consistent with the cavitation collapse core area, and the damage morphology exhibits typical metallic brittleness characteristics—clear and sharp boundaries, and the degree of damage rapidly reaches its maximum value (γ=1) in the collapse center area. Figure 5 (c) Further, it is shown that as the calculation time progresses, the damaged area expands in a strip-like pattern, the early damaged area remains unchanged while new damaged areas continue to be generated at the front end of the hydrofoil, accurately reproducing the dynamic process of "peeling-expansion" of aluminum cavitation. Figure 5 (d) shows that there are more shallow erosion pits in the middle part of the hydrofoil.

[0090] In summary, the cavitation erosion simulation method based on the porosity variation of porous media provided in this application fully considers the cumulative effect and irreversible characteristics of metal material damage by relating dynamic irreversible porosity to local fluid pressure, thus overcoming the technical deficiency of traditional fluid-structure interaction models that cannot reflect the vicious cycle mechanism of "cavitation erosion-cavitation". Specifically for aluminum materials: 1) A relatively high damage threshold of 241 MPa is set to avoid the influence of the high-pressure zone at the hydrofoil tip on the cavitation erosion simulation while reflecting the critical pressure for metal resistance to cavitation erosion; 2) A 1e... 15 The invention simulates the properties of dense aluminum by using kg / m³s viscous resistance; and recreates the cumulative process of metal plastic deformation through the UDM irreversible constraint mechanism. This invention provides an efficient and reliable numerical platform for predicting the cavitation life and optimizing the corrosion resistance design of hydraulic machinery components (ship propellers, pump impellers, etc.).

[0091] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the invention.

Claims

1. A method for simulating the dynamic failure process of material cavitation based on porosity variation, characterized in that, include: Import the computational domain mesh of the material to be tested into the modeling software, and configure the water-vapor multiphase flow model, turbulence model and boundary conditions; A thin mesh region is marked on the surface of the computational domain mesh of the material under test as a damage layer, and the computational domain is cut by domain segmentation. Determine the cavitation model; Standard initialization and setting the initial porosity of the damaged layer to 0; A porous media flow control model is constructed; the porous media flow control model is used to simulate cavitation erosion damage by utilizing the change in porosity of the material under test. A porous media flow control model is introduced into the damaged layer, and a user-defined function is used to dynamically correlate porosity with local pressure values. The introduction of a porous media flow control model into the damaged layer includes: defining the potential cavitation damage region in the material as a porous media region; setting the porosity using a porous media model; and characterizing the material damage process as a dynamic change in porosity from 0 to 1; the dynamic correlation of porosity with local mixed-phase pressure values ​​using a user-defined function includes: Obtain the porosity γ at the current time step current and the largest historical gamma histmax ; At each time step, the fault layer mesh cells are traversed according to the local mixed phase pressure value C. P Determine the porosity at the current time step; if C P If the stress is greater than the yield stress of the material being tested, then let γ be... new = 1.0, indicating the formation of cavitation pits; otherwise γ new = 0.0 indicates that the material is intact, that is In the formula, C P (i,t) represents the local mixed-phase pressure of element i at time t, σ y γ is the yield stress of the material. new (i,t) represents the new porosity state calculated based on the current pressure; Set the γ of the current unit current The value is set to γ new Compared with the historical maximum value γ histmax The larger one in the middle, and update γ. histmax : ; Calculate the γ of the current unit current The value is assigned to the porosity variable; Perform calculations and plot a contour map of the porosity of the material to be tested.

2. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 1, characterized in that, In the water-vapor multiphase flow model, liquid water is the main phase and water vapor is the secondary phase.

3. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 1, characterized in that, The boundary conditions include the boundary surface, velocity inlet, turbulence intensity, hydraulic diameter, liquid water volume fraction, and pressure outlet static pressure.

4. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 1, characterized in that, The cavitation model is as follows: In the formula, ν Let α be the vapor phase, and α be the vapor phase volume fraction. Represents the vector differential operator. For vapor density, For vapor phase velocity, , These are the mass transfer source terms related to the growth and collapse of steam bubbles in cavitation.

5. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 4, characterized in that, In the cavitation model When evaporating, : When it solidifies : in, and These are the empirical calibration coefficients for evaporation and condensation, respectively. ρ l The density of the liquid phase is... ρ For the density of the mixture, Where is the bubble radius. P For local far-field pressure, This refers to the steam pressure.

6. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 1, characterized in that, The method for constructing a porous medium model includes: introducing mass source terms and momentum source terms into the standard fluid flow control equations to obtain the porous medium flow control equations.

7. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 6, characterized in that, The control equations for the flow of porous media include the continuity equation, the momentum equation, and the energy equation. The formula for the continuity equation is: The formula for the momentum equation is: The formula for the energy equation is: In the above three formulas: t is time, γ is porosity, and α is... q It is the volume fraction of phase q, ρ q It is the density of the q phase. d is the velocity vector of phase q, q and d are phase labels used to distinguish different fluid phases, and n is the total number of phases in the system. and These are the mass transfer rates from phase d to phase q and from phase q to phase d, respectively; S q It is the mass source term of phase q; p is the liquid pressure, p c It is the capillary pressure of the wetting phase. It is the shear stress tensor of phase q. It is a volume force. μ q S is the dynamic viscosity coefficient of phase q. i It is a momentum source term. It is the drag force in the non-porous flow / region. It is turbulent dispersion force. It is the velocity vector of phase d relative to phase q. It is the velocity vector of phase q relative to phase d; , , These represent the external volume force, lift force, and virtual mass force acting on the q phase, respectively; s represents the solid material; h q It is the enthalpy of phase q, h s It is the enthalpy of the solid phase; k is the thermal conductivity, k q It is the thermal conductivity of the q phase, k s It is the thermal conductivity of a solid material; p q It is the pressure of phase q, Q dq It is the heat transfer between phase d and phase q, ρ is the density, and T is the heat transfer between phases d and q. q It is the temperature of phase q. h is the energy source term. dq and h qd These are the enthalpy differences corresponding to mass transfer from phase d to phase q and from phase q to phase d, respectively.

8. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 7, characterized in that, The formula for the momentum source term is: In the formula, S i It is the first i The source term of the momentum equation, i = x, y, or z; K is the absolute penetration rate, K r,q C1 is the relative permeability of phase q, and C2 is the inertial drag factor.

9. The method for simulating the dynamic cavitation failure process of materials based on porosity changes according to claim 1, characterized in that, The cloud map illustrates the destructive process and damage area of ​​cavitation on the simulated material through the spatial distribution change of porosity from zero to complete destruction.

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