Numerical prediction method of three-dimensional hydrofoil cavitation erosion damage based on nonlinear cavitation model

Abstract

The application discloses a three-dimensional hydrofoil cavitation erosion damage numerical prediction method based on a nonlinear cavitation model, comprising the following steps: constructing a three-dimensional hydrofoil flow field calculation domain; dividing the calculation domain into grids, and simultaneously defining the boundary positions of the calculation domain inlet and outlet, solid wall surface and symmetry surface; importing the calculation domain grid into a computational fluid dynamics simulation software, checking the grid quality and performing scale reduction; setting the boundary conditions, solving algorithm of the hydrofoil cavitation calculation, and importing the cavitation model; obtaining the hydrofoil surface cavitation periodic evolution law and cavitation erosion damage distribution characteristics through cavitation erosion prediction; comparing the calculation results of the cavitation erosion with the published test results, and correcting the hydrofoil cavitation model. The application realizes reliable and efficient prediction of the material surface damage of the three-dimensional hydrofoil under cloud cavitation conditions, provides theoretical support for revealing the cavitation erosion mechanism induced by unsteady water power cavitation, and enriches the prediction means of the cavitation erosion problem of the water power machinery with the airfoil as the basic blade unit.

Description

Technical Field

[0001] This invention belongs to the field of cavitation detection of bladed hydraulic machinery, specifically involving a three-dimensional numerical prediction method for cavitation damage of hydrofoils based on a nonlinear cavitation model. Background Technology

[0002] Cavitation is a complex multiphase flow involving phase change, turbulence, and compressibility, typically manifested as the formation, growth, and collapse of cavitation bubbles. Cavitation is a unique fluid dynamics problem in hydraulic machinery such as impeller pumps, turbines, reversible turbines, and propellers, where liquids are the working medium. To date, scholars unanimously agree that cavitation processes within hydraulic machinery are harmful. First, cavitation leads to flow channel blockage, significantly reducing the hydraulic performance of the machinery. Second, cavitation affects the unsteady characteristics or dynamic response of the flow, causing instability within the fluid, such as rotational cavitation and cavitation surge. Finally, cavitation damages the surface materials of flow components, resulting in cavitation erosion, accompanied by cavitation vibration and noise. Cavitation-induced cavitation erosion damage is the most damaging and urgently needs to be addressed problem in the field of hydraulic machinery. Applying high-performance anti-cavitation materials is one of the most direct and effective ways to solve this problem. Furthermore, numerical calculations can predict the potential areas and extent of cavitation erosion. Developing corresponding cavitation erosion prediction methods can not only provide optimization strategies during the hydraulic machinery design phase but also accurately predict its operational lifespan, clarify maintenance cycles, and prevent the paralysis of the entire unit system. Therefore, the research and implementation of cavitation erosion prediction methods have significant engineering and academic value for in-depth exploration of hydraulic cavitation-mediated material damage.

[0003] In recent years, commonly used methods for cavitation erosion prediction mainly utilize the pressure changes generated by cavitation collapse on solid surfaces or the microjets formed by near-wall cavitation collapse. Some researchers have also conducted cavitation erosion prediction from the perspective of energy transfer. Furthermore, some scholars have obtained relevant information such as flow field velocity and pressure through Reynolds-averaged numerical simulations and combined this with established erosion depth equations to quantitatively predict the degree of cavitation erosion. Others have directly used experimentally measured cavitation collapse impact pressures obtained from solid surfaces as input parameters for cavitation erosion prediction. However, currently, there is no cavitation erosion prediction model applicable to complex fluid machinery. At the same time, since the prediction methods of cavitation erosion numerical simulations are mainly based on data provided by numerical simulations of cavitation flow fields, their accuracy and stability depend on the accuracy and universality of the cavitation model and the turbulence model.

[0004] Therefore, it is necessary to research and develop excellent numerical models for cavitation erosion to improve the accuracy of cavitation erosion prediction. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned problems by proposing a three-dimensional numerical prediction method for cavitation erosion damage of hydrofoils based on a nonlinear cavitation model. This method can accurately simulate the spatiotemporal evolution of unstable cloud cavitation on hydrofoils and calculate the energy contained within the cavitation bubble using cavitation flow field parameters such as instantaneous pulsating pressure and the rate of change of cavitation radius. This energy is then used as a predictive indicator for cavitation erosion damage. This provides an efficient and feasible numerical model for cavitation-induced cavitation erosion problems in hydraulic machinery with airfoils as the basic blade unit, and promotes the design and engineering application of bladed hydraulic turbines with high cavitation resistance.

[0006] The technical solution of this invention is a three-dimensional numerical prediction method for hydrofoil cavitation damage based on a nonlinear cavitation model, comprising the following steps:

[0007] Step 1: Construct the computational domain for the three-dimensional flow field around the hydrofoil;

[0008] Step 2: Mesh the computational domain from Step 1, and define the domain inlet / outlet, solid walls, and symmetry plane boundaries.

[0009] Step 3: Import the mesh obtained in Step 2 into the computational fluid dynamics simulation software, check the mesh quality and scale it.

[0010] Step 4: Set the boundary conditions and solution algorithm for hydrofoil cavitation calculation, and import the numerical model of cavitation erosion;

[0011] Step 5: Calculate the cavitation distribution characteristics and cavitation erosion damage distribution characteristics of the hydrofoil surface through cavitation flow field calculation;

[0012] Step 6: Compare the calculation results of cavitation erosion in Step 5 with the published experimental results, and correct the numerical model of hydrofoil cavitation erosion based on the comparison results.

[0013] Preferably, in step 1, the calculation domain for the hydrofoil cavitation flow field is constructed by using the 3D modeling software Solidworks to model the external fluid region of the hydrofoil.

[0014] Preferably, step 2 includes the following sub-steps:

[0015] Step 2.1: Import the computational domain file from Step 1 into the network partitioning software ICEMCFD, and name the boundaries of the computational domain;

[0016] Step 2.2: Construct the initial topological block structure of the mesh. By appropriately dividing the block structure of the hydrofoil surface, the block structure is made independent and externally divided into "O" shapes. Then, the number of mesh nodes is set according to the line length on the computational domain. The "O" shape blocks are set with a sufficiently dense mesh along their normal direction so that the body-fitting mesh is located within the boundary layer.

[0017] Preferably, in step 3, the mesh is imported into the computational fluid dynamics simulation software, and the mesh file obtained in step 2 is read using ANSYS FLUENT, which is then reduced to 1 / 1000 of the original size, and the mesh quality is checked to see if it meets the calculation requirements.

[0018] Preferably, step 4 includes the following sub-steps:

[0019] Step 4.1: Select unsteady mode as the solver and set the turbulence model to the large eddy simulation method;

[0020] Step 4.2: Construct cavitation damage indices, establish hydrofoil cavitation model and cavitation numerical model, and compile and embed them into simulation software respectively;

[0021] Step 4.3: Set the working fluid to liquid water and cavitation, and set the main properties of the two according to the corresponding temperature. The inlet of the computational domain is the velocity inlet boundary, the outlet of the computational domain is the pressure outlet boundary, the middle section is the symmetry plane, and the rest are solid wall boundaries.

[0022] Step 4.4: Set the pressure-velocity coupling mode to SIMPLEC format, select a high-order interpolation format for physical quantities such as gradient, pressure, momentum, and volume fraction, and set the convergence residual criterion to 1×10⁻⁶. -6 .

[0023] Preferably, in step 4.2, the hydrofoil cavitation model is a nonlinear cavitation model that considers non-condensable gases and vortex effects. The mathematical expression of the cavitation model is as follows:

[0024]

[0025] In the formula, R e R c Representing evaporation rate and condensation rate respectively, n0 is the cavitation nucleus density, ρ l ρ v ρ g ρ m α represents the density of the liquid phase, cavitation phase, non-condensable gas, and mixed fluid, respectively. l α v α g R represents the volume fractions of the liquid phase, cavitation phase, and non-condensable gas, respectively. b r0 represents the initial radius of the cavitation bubble, and p represents the radius of the cavitation bubble. v F represents the vaporization pressure, p is the static pressure of the flow field, and F is the vaporization pressure. r Let p be a rotation function. sat Let f be the saturated vapor pressure of the liquid phase, k be the turbulent kinetic energy, and f be the saturated vapor pressure of the liquid phase. g U represents the mass fraction of non-condensable gases. ∞ For characteristic velocity, L ∞f is the characteristic length. rotation This represents the rotation factor, and max() represents the function to find the maximum value.

[0026] In step 4.2, the cavitation damage index is a numerical model based on the energy contained in cloud cavitation, and its mathematical expression is as follows:

[0027]

[0028] In the formula, <E cav > represents the overall index of cavitation damage, T represents the calculation time period, and e represents the value of e. pot (t) is the instantaneous spatial erosion function in the computational domain, where t represents time, and E pot-cell p represents the instantaneous cavitation erosion on a single grid cell. d For cavitation driving pressure, p v The vaporization pressure is represented by p, the static pressure of the flow field is n0, and the cavitation nucleus density is r. b ρ represents the cavitation radius, r0 represents the initial cavitation radius, and ρ l ρ m p represents the density of the liquid phase and the mixed fluid, respectively. sat Let be the saturated vapor pressure of the liquid phase, and k be the turbulent kinetic energy.

[0029] Furthermore, step 6 specifically includes the following sub-steps:

[0030] 1) The cloud cavitation evolution process within one cycle of the hydrofoil was obtained through the CFD-POST post-processing program and compared with the experimental results obtained by high-speed camera under the same operating conditions;

[0031] 2) The distribution law of cavitation damage on the hydrofoil surface was obtained by CFD-POST post-processing program and compared with the cavitation test results obtained by paint test under the same operating conditions.

[0032] 3) Based on the comparison results, verify the accuracy and feasibility of the numerical prediction method for cavitation damage of three-dimensional hydrofoils based on the nonlinear cavitation model, and correct the cavitation prediction method.

[0033] Compared with the prior art, the beneficial effects of the present invention include:

[0034] 1. This invention employs a nonlinear cavitation model to capture the periodic cavitation evolution of the hydrofoil surface, achieving high computational accuracy and providing reliable flow field parameters such as pressure and cavitation volume fraction for cavitation erosion calculation.

[0035] 2. The numerical prediction method for hydrofoil cavitation damage of the present invention realizes reliable and efficient prediction of surface damage of three-dimensional hydrofoil materials under cloud cavitation conditions, provides theoretical support for revealing the mechanism of cavitation induced by unsteady hydraulic cavitation, and enriches the prediction means for hydraulic mechanical cavitation cavitation problems with airfoils as the basic blade unit.

[0036] 3. This invention uses experimental measurements to verify and correct the predicted results of cavitation erosion on the hydrofoil surface, making the cavitation erosion simulation results more reliable. Attached Figure Description

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0038] Figure 1 This is a schematic diagram of the numerical prediction process for hydrofoil cavitation erosion according to an embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram of the hydrofoil cavitation erosion calculation domain according to an embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram of the symmetry plane mesh of the hydrofoil cavitation erosion calculation domain in an embodiment of the present invention.

[0041] Figure 4 This is a schematic diagram comparing the numerical calculation of the periodic evolution of hydrofoil cavitation with the results of high-speed photography in an embodiment of the present invention.

[0042] Figure 5a This is a schematic diagram of the hydrofoil cavitation damage prediction results according to an embodiment of the present invention.

[0043] Figure 5b This is a schematic diagram of the paint cavitation damage test results of the hydrofoil according to an embodiment of the present invention. Detailed Implementation

[0044] The embodiment uses the publicly disclosed three-dimensional Delft Twist-11 twisted hydrofoil as the object. The hydrofoil has a cross-section of NACA0009 airfoil, a chord length of c = 0.15m, and a wingspan of L = 2c = 0.3m.

[0045] like Figure 1 As shown, the numerical prediction method for cavitation damage of a three-dimensional hydrofoil based on a nonlinear cavitation model includes the following steps:

[0046] Step 1: Construct the computational domain for the three-dimensional flow field around the hydrofoil;

[0047] like Figure 2As shown, the computational domain for cavitation erosion of the Delft Twist-11 twisted hydrofoil is a cuboid in shape, with the three-dimensional hydrofoil located inside. The total length, width, and height of the computational domain are 6c, c, and 2c, respectively, and the distance from the leading edge of the hydrofoil to the inlet is 2c. The external flow field of the hydrofoil was modeled in 3D using the Solidworks 3D modeling tool, and the final computational domain was saved as a step format transfer file.

[0048] Step 2: Mesh the computational domain from Step 1, and define the locations of the inlet / outlet, solid walls, and symmetry plane boundaries. A schematic diagram of the computational domain symmetry plane mesh is shown below. Figure 3 As shown;

[0049] Step 2.1: Import the computational domain file from Step 1 into the network partitioning software ICEMCFD. Referring to the water flow direction, define the inlet boundary, outlet boundary, three solid wall boundaries, and one symmetry plane of the computational domain to complete the boundary naming of the computational domain.

[0050] Step 2.2: Create the initial topology block structure of the mesh. By appropriately dividing the block structure of the hydrofoil surface, separate it into independent blocks and perform external O-sections. Then, set the number of mesh nodes according to the line length on the computational domain. Set a sufficiently dense mesh for the O-blocks along their normal direction. Set the thickness of the first mesh layer to 1μm so that the body-fitting mesh is located within the boundary layer. Output the msh file.

[0051] Step 3: Import the mesh file obtained in Step 2 into the computational fluid dynamics simulation software, check the mesh quality and scale it.

[0052] Use ANSYS FLUENT software to read the mesh file obtained in step 2, scale it down to 1 / 1000 of its original size using the Scale Factor command, and use the Check command to check the mesh quality to determine whether it meets the calculation requirements.

[0053] Step 4: Set the boundary conditions and solution algorithm for hydrofoil cavitation calculation, and import the cavitation erosion model;

[0054] Step 4.1: Select unsteady mode as the solver and set the turbulence model to the large eddy simulation method;

[0055] Step 4.2: Establish the hydrofoil nonlinear cavitation model and cavitation damage numerical model, and compile them using user-defined functions and embed them in ANSYS FLUENT software respectively;

[0056] Step 4.3: Set the working fluid to liquid water and cavitation, with the density and viscosity of liquid water being ρ and ρ, respectively. l =1000kg / m 3 μ l=1.139×10 -3 Pa.s; the density and viscosity of the cavitation bubbles are ρ. v =0.02308kg / m 3 μ v =9.8626×10 -6 Pa.s. The inlet boundary of the computational domain is set as a velocity condition with a magnitude of U = 6.97 m / s; the outlet boundary is set as a pressure condition with a magnitude of p. out =29159.7Pa, the top, bottom and one side of the computational domain are solid walls, and the middle section is a symmetry plane boundary;

[0057] Step 4.4: Set the pressure-velocity coupling mode to SIMPLEC format, the gradient interpolation to Green-GaussNode Based format, the pressure interpolation to Pressure Staggering Option (PRESTO!) format, the momentum interpolation to Bounded Central Differencing format, and the volume fraction to QUICK format. Set the convergence residual criterion for all physical quantities to 1×10⁻⁶. -6 To improve calculation accuracy.

[0058] Step 5: Calculate the cavitation distribution characteristics and cavitation erosion damage distribution characteristics of the hydrofoil surface through cavitation flow field calculation;

[0059] Step 6: Compare the calculation results of cavitation erosion in Step 5 with the corresponding published experimental results. The experimental results use high-speed cameras to capture the evolution of cloud cavitation and paint experiments to record the cavitation erosion area and its severity. The numerical model of hydrofoil cavitation erosion is corrected based on the comparison results.

[0060] In step 4.2, the cavitation model is a nonlinear cavitation model that considers non-condensable gases and vortex effects. The mathematical expression of the model is as follows:

[0061]

[0062] In the formula, R e With R c These represent the evaporation rate and condensation rate, respectively, where n0 is the cavitation nucleus density, and r... b r0 and r0 are the cavitation radius and initial cavitation radius, respectively, ρ is the density, α is the volume fraction, and p v p represents the vaporization pressure and the static pressure of the flow field, respectively. The subscripts l, v, g, and m represent the liquid phase, cavitation phase, non-condensable gas, and mixed fluid, respectively. F r Let p be a rotation function. sat Let f be the saturated vapor pressure of the liquid phase, k be the turbulent kinetic energy, and f be the saturated vapor pressure of the liquid phase. g U represents the mass fraction of non-condensable gases. ∞For characteristic velocity, L ∞ f is the characteristic length. rotation is the rotation factor.

[0063] The cavitation damage index is a numerical model based on the energy contained in cloud cavitation bubbles, and its mathematical expression is as follows:

[0064]

[0065] In the formula, <E cav > represents the overall index of cavitation damage, T represents the calculation time, and e represents the time interval. pot To calculate the instantaneous cavitation erosion in the calculation domain, E pot-cell p represents the instantaneous cavitation erosion on each grid cell. d For cavitation driving pressure, p v p and n0 are the vaporization pressure and static pressure of the flow field, respectively, and n0 is the cavitation nucleus density. b Let r0 be the cavitation radius and r0 be the initial cavitation radius, respectively, and ρ be the cavitation radius. l With ρ m These represent the densities of the liquid phase and the mixed fluid, respectively, p. sat Let be the saturated vapor pressure of the liquid phase, and k be the turbulent kinetic energy.

[0066] In step 6, CFD-POST post-processing is used to obtain the periodic cloud cavitation evolution and corresponding cavitation damage distribution on the surface of the three-dimensional DelftTwist-11 twisted hydrofoil under the same operating conditions, and the results are compared with experimental values. Figure 4 As shown in the figure. The hydrofoil cavitation damage prediction results and paint test results of the embodiment are respectively as follows. Figure 5a , 5b As shown in the figure, the comparison shows that the nonlinear cavitation model combined with the large eddy simulation method can accurately capture the periodic evolution of cloud cavitation on the hydrofoil surface. More importantly, the numerical calculation prediction of cavitation damage results matches the paint experiment results well. The cavitation erosion area is mainly located in the middle of the airfoil surface, which verifies the accuracy and feasibility of the numerical prediction method of the present invention.

[0067] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the numerical algorithm and principle of the present invention should be included within the scope of protection of the present invention.

Claims

1. A numerical prediction method for cavitation damage of a three-dimensional hydrofoil based on a nonlinear cavitation model, characterized in that, Includes the following steps, Step 1: Construct the computational domain for the three-dimensional flow field around the hydrofoil; Step 2: Mesh the computational domain from Step 1 and define the inlet / outlet, solid walls, and symmetry plane boundaries of the computational domain; Step 3: Import the computational domain mesh obtained in Step 2 into the computational fluid dynamics simulation software; Step 4: Set the boundary conditions and solution algorithm for hydrofoil cavitation calculation, and import the numerical model of cavitation erosion; Step 4.1: Set the solver to unsteady mode and set the turbulence model to the large eddy simulation method model; Step 4.2: Construct a cavitation damage index based on the energy contained in cloud cavitation, establish a cavitation model, and compile it; Step 4.3: Set the working fluid to liquid water and cavitation, set the properties of liquid water and cavitation, set the computational domain inlet to velocity inlet boundary, the computational domain outlet to pressure outlet boundary, the intermediate section to symmetry plane, and the rest to solid wall boundary; Step 4.4: Set the pressure-velocity coupling mode, and select a higher-order format for the interpolation of gradient, pressure, momentum, and volume fraction; Step 5: Calculate the cavitation distribution characteristics and cavitation erosion damage distribution characteristics of the hydrofoil surface through cavitation flow field calculation; In step 4.2, the mathematical expression of the cavitation model is as follows: ； In the formula, R e R c represents the evaporation rate and condensation rate, respectively. For cavitation nuclei density, , , , These represent the densities of the liquid phase, cavitation phase, non-condensable gas, and mixed fluid, respectively. , , These represent the volume fractions of the liquid phase, cavitation phase, and non-condensable gas, respectively. Indicates the cavitation radius, Indicates the initial radius of the cavitation bubble. Indicates vaporization pressure, p For static pressure in the flow field, F r is the rotation function. This is the saturated vapor pressure of the liquid phase. k For turbulent kinetic energy, f g represents the mass fraction of non-condensable gases. Characteristic velocity, For characteristic length, This represents the rotation factor, and max() represents the function to maximize the value. In step 4.2, the mathematical expression for the cavitation damage index is as follows: ； In the formula, < E cav> is an overall index of cavitation damage. T To calculate the time period, To compute the instantaneous spatial erosion function in the computational domain, t Indicates time, E pot-cell represents the instantaneous cavitation on a single grid cell. Cavitation-driven pressure, Indicates vaporization pressure, p For static pressure in the flow field, For cavitation nuclei density, Indicates the cavitation radius, Indicates the initial radius of the cavitation bubble. , These represent the densities of the liquid phase and the mixed fluid, respectively. This is the saturated vapor pressure of the liquid phase. k It is turbulent kinetic energy.

2. The three-dimensional hydrofoil cavitation damage numerical prediction method according to claim 1, characterized in that, The method further includes step 6: comparing the calculation results of cavitation erosion in step 5 with the published experimental results, and correcting the numerical model of hydrofoil cavitation erosion based on the comparison results.

3. The three-dimensional hydrofoil cavitation damage numerical prediction method according to claim 1, characterized in that, In step 1, the calculation domain of the hydrofoil cavitation flow field is constructed, and the external fluid region of the hydrofoil is modeled using the 3D drawing software Solidworks.

4. The three-dimensional hydrofoil cavitation damage numerical prediction method according to claim 1, characterized in that, Step 2 includes the following sub-steps: Step 2.1: Import the computational domain file from Step 1 into the network partitioning software ICEM CFD, and name the boundaries of the computational domain; Step 2.2: Construct the initial topological block structure of the mesh. Make the block structure of the hydrofoil surface independent of each other by appropriate partitioning and perform external "O"-shaped partitioning on it. Then, set the number of mesh nodes according to the line length on the computation domain, and set a sufficiently dense mesh for the "O"-shaped block along its normal direction so that the body mesh is located within the boundary layer.

5. The three-dimensional hydrofoil cavitation damage numerical prediction method according to claim 1, characterized in that, In step 3, the mesh file obtained in step 2 is read using ANSYS FLUENT, reduced to 1 / 1000 of its original size, and the mesh quality is checked to see if it meets the calculation requirements.

6. The three-dimensional hydrofoil cavitation damage numerical prediction method according to claim 1, characterized in that, Step 6 specifically includes: 1) The cloud cavitation evolution process within one cycle of the hydrofoil was obtained through the CFD-POST post-processing program and compared with the experimental results obtained by high-speed camera under the same operating conditions; 2) The distribution law of cavitation damage on the hydrofoil surface was obtained by CFD-POST post-processing program and compared with the cavitation test results obtained by paint test under the same operating conditions. 3) Based on the comparison results, verify the accuracy and feasibility of the numerical prediction method for cavitation damage of three-dimensional hydrofoils based on the nonlinear cavitation model, and correct the cavitation prediction method model.

7. The three-dimensional hydrofoil cavitation damage numerical prediction method according to any one of claims 1-6, characterized in that, In step 4.4, the convergence residual standard is set to 1×10⁻⁶. -6 .

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