A method for correcting cavitation models for rapid prediction of vortex cavitation

Abstract

This invention discloses a cavitation model correction method for rapid prediction of vortex cavitation. The correction method identifies vortex boundaries using vortex identification criteria, dividing the flow field into vortex interior and exterior. The correction module consists of a damping function and a pressure correction function. The damping function primarily provides a shielding effect, while the pressure correction function primarily corrects the pressure. Both functions simultaneously correct the pressure inside the vortex. This invention can predict vortex cavitation phenomena with relatively coarse grid resolution, thus achieving rapid cavitation prediction with reduced computational resource costs. It has significant practical engineering application and promotion value.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic machinery technology, and specifically relates to a cavitation model correction method for rapidly predicting vortex cavitation. Background Technology

[0002] Cavitation is an important and complex phenomenon in hydrodynamics, and it often has adverse effects, such as reduced mechanical efficiency, increased noise and vibration, and even structural damage. There are many ways to classify cavitation, among which vortex cavitation, a special type, typically occurs in the strong shear region within a vortex. Strong vortex structures contain significant pressure gradients, forming a low-pressure region at the vortex core. When the pressure at the vortex core falls below the saturated vapor pressure, cavitation occurs. Examples of typical vortex cavitation phenomena include blade passage vortex cavitation in rotating turbine runners, draft tube vortex cavitation, propeller tip vortex cavitation, and tip clearance leakage vortex cavitation.

[0003] Currently, the industry primarily uses numerical simulations to predict vortex cavitation within hydraulic machinery. However, commonly used cavitation prediction models (such as the ZGB cavitation model and the Schnerr-Sauer cavitation model) have high computational resource requirements, mainly due to the need for high grid resolution. Insufficient grid resolution in these models can lead to an underestimation of vortex cavitation, hindering their widespread engineering application. Summary of the Invention

[0004] To address the problems in the background technology and handle vortex cavitation scenarios, this invention proposes a cavitation model correction method for rapid prediction of vortex cavitation, which is independent of grid resolution. The goal of this invention is to solve two major problems in the study of hydraulic mechanical cavitation phenomena: high experimental costs and limited acquisition of fine flow field information. The key advantage of this method lies in its ability to improve the accuracy of vortex cavitation prediction using low-resolution grids, providing a more effective approach to solving cavitation problems and possessing significant engineering application value.

[0005] The technical solution adopted in this invention is as follows, including the following steps:

[0006] Step 1: Identify vortex boundaries using the vortex identification criterion. Based on the vortex boundaries, divide the flow field into an inner vortex region and an outer vortex region. When the vortex identification criterion is greater than or equal to a set threshold, it is considered an inner vortex region; when the vortex identification criterion is less than the set threshold, it is considered an outer vortex region. The vortex identification criterion is the omega vortex identification criterion.

[0007] Step 2: Based on the pressure correction function P CPThe pressure value of the cavitation model in the internal region of the vortex is corrected, and the corrected pressure value P C The expression is:

[0008] P C =C r1 f D P CP

[0009] Among them, C r1 f is a given constant, which in practice takes values ​​from 6 to 8; D P represents the damping function; CP This represents the pressure correction function;

[0010] The pressure values ​​of the cavitation model in the outer region of the vortex remain the same as the original cavitation model values.

[0011] This involves implementing a cavitation model correction for rapid prediction of vortex cavitation.

[0012] In practice, the main correction involves adjusting the predicted pressure values ​​for the internal region of the vortex, thereby improving the accuracy of vortex cavitation estimation using a low-resolution grid. This correction primarily utilizes a damping function f. D and a pressure correction function P CP Together they constitute the damping function f. D Its main function is shielding, to block the correction effect generated in non-vortex regions. Pressure correction function P CP Its main function is to correct pressure.

[0013] In step two, the damping function is mainly used to shield the external region of the vortex, thereby producing a correction effect. The damping function f D The expression is:

[0014] f D =tanh(C r1 Ω-C r1 )+C r2

[0015] In the formula, C r2 is a given constant, which takes the value of 1 to 2 in specific implementations; Ω is a commonly used omega vortex identification criterion in this field, which will not be described in detail.

[0016] In step two, the pressure correction function P CP Primarily used for correcting pressure values, the pressure correction function P CP The expression is:

[0017]

[0018] In the formula, C g1C is a given constant, which is taken as 5622 in the specific implementation; g2 is a given constant, which is taken as 5 in the specific implementation; Δ is the grid scale, which is the cube root of the local grid volume in 3D and the square root of the local grid volume in 2D; L0 is the hydraulic characteristic dimension; u ∞ ρ is the incoming flow velocity; ρ is the fluid density.

[0019] The cavitation model includes a mass transfer model based on the Rayleigh-Plesset equation, which ignores thermal effects, surface tension, and higher-order derivatives.

[0020] The mass transfer models include the ZGB cavitation model and the Schnerr-Sauer cavitation model.

[0021] In the field of hydraulic machinery, numerical simulation is generally used to predict and evaluate cavitation phenomena generated inside hydraulic machinery. Mesh generation is a crucial step in numerical simulation; the finer the mesh resolution, the higher the accuracy of the numerical simulation, but the higher the computational resource consumption. The cavitation model, as another aspect of numerical simulation, is also closely related to mesh generation. Currently, commonly used cavitation prediction models in engineering, such as the ZGB cavitation model and the Schnerr-Sauer cavitation model, all exhibit a high dependence on mesh resolution, especially when predicting vortex cavitation. Insufficient mesh resolution leads to overestimation of the predicted pressure values ​​inside the vortex, resulting in a significant underestimation of vortex cavitation. Therefore, correcting the pressure values ​​inside the vortex improves the accuracy of pressure prediction, thereby enhancing the accuracy of simulating real-world conditions using low mesh resolution. This invention improves the prediction accuracy of vortex cavitation by using a damping function and a pressure correction function to correct the pressure values ​​inside the vortex. The damping function f... D The Omega vortex identification criterion is used to identify local flow field information and establish vortex boundaries, thus achieving a shielding effect. In the Omega vortex identification criterion, a dimensionless parameter Ω greater than 0.5 indicates the presence of vortices, and the damping function f... D The value of Ω is approximately 0 in the region where Ω is less than 0.5, indicating that the correction of this invention is ineffective in the vortex-free region. Pressure correction function P CP The purpose is to identify the mesh resolution and apply corresponding corrections. The pressure correction function P CP Based on grid identification factor f GAF Adjust the correction intensity, grid identification factor f GAF A larger value indicates insufficient grid resolution, and the corresponding pressure correction function P CP The larger the value, the better. The simultaneous application of the damping function and the pressure correction function can improve the accuracy of the corrected pressure value, thereby enhancing the ability to predict vortex cavitation when the grid resolution is insufficient, ultimately enabling rapid prediction of vortex cavitation.

[0022] This invention designs a cavitation model correction method for rapidly predicting vortex cavitation, and further includes the following steps: using the cavitation model obtained in the above steps to predict the characteristics of the vortex cavitation flow field, providing guidance for flow analysis and structural optimization, improving the performance of hydraulic machinery systems, reducing costs, and enhancing reliability. The obtained cavitation flow field information is also applicable to engineering health diagnosis, helping to solve problems in a timely manner and improve equipment reliability and safety. The method proposed in this invention has innovative potential in multiple fields and is of great significance for improving system performance, reducing costs, and extending equipment life.

[0023] The beneficial effects of this invention are:

[0024] 1. The present invention proposes a cavitation model correction method for rapid prediction of vortex cavitation, which corrects the predicted pressure value inside the vortex, thereby improving the prediction accuracy of vortex cavitation.

[0025] 2. The present invention proposes a cavitation model correction method for rapid prediction of vortex cavitation, which improves the accuracy of vortex cavitation prediction by low-resolution grids, thereby achieving the effect of saving computational costs.

[0026] 3. The cavitation model correction method disclosed in this invention for rapidly predicting vortex cavitation can be applied to the numerical prediction of various vortex cavitation problems.

[0027] 4. The cavitation model correction method disclosed in this invention for rapidly predicting vortex cavitation can provide guidance for flow analysis and structural optimization, and provide technical support for improving the performance of hydraulic machinery systems, reducing costs, and enhancing reliability. Attached Figure Description

[0028] Figure 1 This is a flowchart of the cavitation model correction method for rapidly predicting vortex cavitation according to the present invention;

[0029] Figure 2 The damping function f of the cavitation model correction method for rapid prediction of vortex cavitation in this invention is... D Line graph;

[0030] Figure 3 The pressure correction function P of this invention is used in a cavitation model correction method for rapidly predicting vortex cavitation. CP Line graph;

[0031] Figure 4 This is a velocity vector distribution diagram of Example 1 of the present invention (basic flow field inside a two-dimensional Rankine vortex);

[0032] Figure 5 This is a comparison diagram of the model correction effect in Example 1 of the present invention (basic flow field inside a two-dimensional Rankine vortex);

[0033] Figure 6 This is a schematic diagram of the computational domain for Example 2 of the present invention (three-dimensional hydrofoil gap leakage vortex cavitation flow field);

[0034] Figure 7 This is a comparison diagram of the vortex cavitation morphology before and after model correction and the experimental results in working condition one (gap 0.01m) of Example 2 of this invention (three-dimensional hydrofoil gap leakage vortex cavitation flow field);

[0035] Figure 8 This is a comparison diagram of the vortex cavitation morphology before and after model correction and the experimental results in working condition two (gap 0.015m) of Example 2 of this invention (three-dimensional hydrofoil gap leakage vortex cavitation flow field). Detailed Implementation

[0036] The implementation method of the cavitation model correction method for rapidly predicting vortex cavitation according to the present invention will be described in detail with reference to the accompanying drawings.

[0037] The cavitation model correction method of the present invention, such as Figure 1 As shown:

[0038] Step 1: Identify vortex boundaries using the vortex identification criterion. Based on the vortex boundaries, divide the flow field into an inner vortex region and an outer vortex region. When the vortex identification criterion is greater than or equal to a set threshold, it is considered an inner vortex region; when the vortex identification criterion is less than the set threshold, it is considered an outer vortex region. The vortex identification criterion is the omega vortex identification criterion.

[0039] Step 2: Based on the pressure correction function P CP The pressure value of the cavitation model in the internal region of the vortex is corrected, and the corrected pressure value P C The expression is:

[0040] P C =C r1 f D P CP

[0041] Among them, C r1 f is a given constant, which in practice takes values ​​from 6 to 8; D P represents the damping function; CP This represents the pressure correction function;

[0042] The pressure values ​​of the cavitation model in the outer region of the vortex remain the same as the original cavitation model values.

[0043] This involves implementing a cavitation model correction for rapid prediction of vortex cavitation.

[0044] In practice, the main correction involves adjusting the predicted pressure values ​​for the internal region of the vortex, thereby improving the accuracy of vortex cavitation estimation using a low-resolution grid. This correction primarily utilizes a damping function f. D and a pressure correction function P CP Together they constitute the damping function f. D Its main function is shielding, to block the correction effect generated in non-vortex regions. Pressure correction function P CP Its main function is to correct pressure.

[0045] In step two, the damping function is mainly used to shield the outer region of the vortex, thereby producing a correction effect, such as... Figure 2 As shown, the damping function f D The expression is:

[0046] f D =tanh(C r1 Ω-C r1 )+C r2

[0047] In the formula, C r2 is a given constant, which takes the value of 1 to 2 in specific implementations; Ω is a commonly used omega vortex identification criterion in this field, which will not be described in detail.

[0048] In step two, the pressure correction function P CP Primarily used for correcting pressure values, such as Figure 3 As shown, the pressure correction function P CP The expression is:

[0049]

[0050] In the formula, C g1 C is a given constant, which is taken as 5622 in the specific implementation; g2 is a given constant, which is taken as 5 in the specific implementation; Δ is the grid scale, which is the cube root of the local grid volume in 3D and the square root of the local grid volume in 2D; L0 is the hydraulic characteristic dimension; u ∞ ρ is the incoming flow velocity; ρ is the fluid density.

[0051] Cavitation models include mass transfer models based on the Rayleigh-Plesset equations, which neglect thermal effects, surface tension, and higher-order derivatives. Mass transfer models also include the ZGB cavitation model and the Schnerr-Sauer cavitation model.

[0052] Example 1:

[0053] Figure 4This is a velocity vector distribution diagram of the basic flow field inside a two-dimensional Rankine vortex, as described in Example 1 of this invention. Based on this two-dimensional basic flow field, the analytical solution of the pressure inside the two-dimensional vortex can be obtained, allowing for quantitative and qualitative analysis of the correction effect of this invention within the flow field. The flow field parameters of the basic flow field inside the two-dimensional Rankine vortex are as follows: angular velocity ω θ =1, density ρ=1, vortex boundary r0=100. Analytical solution of pressure P inside a two-dimensional Rankine vortex. RV The expression is: P RV =r 2 / 2. The basic idea of ​​the finite volume method is to first integrate and then take the average. Therefore, based on this idea, the pressure value predicted by numerical simulation can be defined as the pressure value predicted by a single grid in the flow field.

[0054]

[0055] In the formula, θ represents the angle in polar coordinates; dθ represents the differential of the angle in polar coordinates; r represents the distance from the vortex center; dr is equivalent to the grid size in polar coordinates; and A represents the grid area.

[0056] Figure 5 This is the basic flow field inside a two-dimensional Rankine vortex in Example 1 of this invention, which uses a comparison between the corrected predicted vortex cavitation region and the analytical solution cavitation region of this invention. In Example 1 of this invention, the values ​​of the model are as follows:

[0057] C r1 =6; C r2 =1; C g1 =5622; C g2 =5; L0=200; ρ=1; u ∞ =1; Δ=40; Ω=1.

[0058] First, calculate the pressure correction function P. CP and damping function f D :

[0059] f D =tanh(C r1 Ω-C r1 )+C r2 =1

[0060]

[0061] Then, using the pressure correction function P CP and damping function f D The internal region of the vortex is corrected, and the corrected pressure value P is obtained. C for:

[0062] P C =Cr1 f D P CP =667.64

[0063] The saturated vapor pressure of the flow field is 3540, indicating that cavitation will occur in regions with pressures below 3540. Analytical solution P RV The lower cavitation region is approximately 0 ≤ r ≤ 84; the pressure value predicted by numerical simulation. The predicted cavitation region is approximately 0 ≤ r ≤ 48; after correction using the model of this invention, the predicted cavitation region is approximately 0 ≤ r ≤ 56. In this two-dimensional Rankine vortex field, the numerical simulation predicts the pressure values. The predicted cavitation region is equivalent to the analytical solution P. RV The predicted 57% cavitation region, after correction using the model of this invention, is equivalent to the analytical solution P. RV The prediction accuracy was 67%, effectively improving the prediction accuracy by 10%.

[0064] Example 2:

[0065] Figure 6 This is a schematic diagram of the computational domain for the three-dimensional hydrofoil gap leakage vortex cavitation flow field in Embodiment 2 of the present invention. The computational domain information includes the inlet, outlet, wall, hydrofoil, and gap. The hydrofoil is a NACA0009 hydrofoil with an angle of attack of 10 degrees. The inlet is a velocity inlet with an inlet velocity of 10 m / s. The outlet is a pressure outlet with an outlet pressure of 1 bar. Two operating conditions are calculated: condition 1 with a gap height of 0.01 m and condition 2 with a gap height of 0.015 m.

[0066] When calculating operating conditions one and two, the values ​​in the model of this invention are as follows: C r1 =6; C r2 =1; C g1 =5622; C g2 =5; L0=0.15; ρ=998; u ∞ =10; the values ​​of Ω and Δ are updated according to the flow field information.

[0067] First, calculate the pressure correction function P. CP and damping function f D :

[0068] f D =tanh(C r1 Ω-C r1 )+C r2 =tanh(6Ω-6)+1

[0069]

[0070] Then, using the pressure correction function P CP and damping function fD The internal region of the vortex is corrected, and the corrected pressure value P is obtained. C for:

[0071]

[0072] Figure 7 This is a comparison of the vortex cavitation morphology and experimental results before and after model correction for Case 1 (gap height 0.01m) in Example 2 of this invention. Based on a low-resolution mesh with approximately 2.2 million meshes in the entire computational domain, numerical simulations were performed using both the original Schnerr-Sauer cavitation model and the cavitation model corrected by this invention. It can be observed that with low mesh resolution, the Schnerr-Sauer cavitation model can almost not predict vortex cavitation, while the cavitation model corrected by this invention can effectively predict the vortex cavitation morphology. In the experimental snapshot, the vortex cavitation length extends to approximately 0.15m. The predicted vortex cavitation length using the Schnerr-Sauer cavitation model is less than 0.01m, while the predicted cavitation length using the cavitation model corrected by this invention reaches the same 0.15m as in the experimental snapshot.

[0073] Figure 8 This is a comparison of the vortex cavitation morphology and experimental results before and after model correction for Case 2 (gap height 0.015m) in Example 2 of this invention. Based on a low-resolution grid with approximately 2.8 million grid cells across the entire computational domain, numerical simulations were performed using both the original Schnerr-Sauer cavitation model and the modified cavitation model of this invention. In the experimental snapshot, the vortex cavitation length extends to approximately 0.15m. The predicted vortex cavitation length using the Schnerr-Sauer cavitation model was less than 0.01m, while the predicted cavitation length using the modified cavitation model of this invention reaches the same 0.15m as in the experimental snapshot.

[0074] The cavitation model correction method of this invention further includes the following steps: using the cavitation model corrected by the above steps to predict the characteristics of the vortex cavitation flow field, providing guidance for flow analysis and structural optimization, improving the performance of hydraulic machinery systems, reducing costs, and enhancing reliability. The obtained cavitation flow field information is also applicable to engineering health diagnosis, helping to solve problems in a timely manner and improve equipment reliability and safety. The method proposed in this invention has innovative potential in multiple fields and is of great significance for improving system performance, reducing costs, and extending equipment lifespan.

[0075] 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 spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A cavitation model correction method for rapid prediction of vortex cavitation, characterized in that: Step 1: Identify vortex boundaries using the vortex identification criterion, and divide the flow field into an internal vortex region and an external vortex region based on the vortex boundaries; the vortex identification criterion is the omega vortex identification criterion. Step 2: Based on the pressure correction function P CP The pressure value of the cavitation model in the internal region of the vortex is corrected, and the corrected pressure value P C The expression is: ; Among them, C r1 f is a given constant; D P represents the damping function; CP This represents the pressure correction function; The pressure values ​​of the cavitation model in the outer region of the vortex remain the same as the original cavitation model values. That is, to correct the cavitation model; In step two, the damping function f D Used to shield the outer region of the vortex, thereby producing a correction effect, damping function f D The following formula is used to obtain the result: ; In the formula, C r2 For a given constant; Omega vortex identification criteria; In step two, the pressure correction function P CP Used for pressure value correction, pressure correction function P CP The following formula is used to obtain the result: ; In the formula, C g1 C is a given constant; g2 For a given constant; L0 is the grid scale; L0 is the hydraulic feature size. The incoming flow velocity; The fluid density is given.

2. The cavitation model correction method for rapidly predicting vortex cavitation according to claim 1, characterized in that: The cavitation model includes a mass transfer model based on the Rayleigh-Plesset equation, which ignores thermal effects, surface tension, and higher-order derivatives.

3. The cavitation model correction method for rapidly predicting vortex cavitation according to claim 2, characterized in that: The mass transfer models include the ZGB cavitation model and the Schnerr-Sauer cavitation model.

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