A numerical simulation method for compressible phase change in cavitation flow

Abstract

The present invention provides a numerical simulation method for a compressible phase change process in a cavitation flow, the implementation process of which includes calculating the liquid phase density and liquid phase sound velocity in the compressible flow; solving the bubble wall velocity during the bubble growth or contraction process based on the liquid phase density, the liquid phase sound velocity, and the Rayleigh-Plesset equation taking into account the liquid phase compressibility; calculating the interphase mass transfer rate based on the bubble wall velocity during the bubble growth or contraction process and the material derivative of the vapor phase density within the bubble, thereby obtaining a phase change model that takes into account the compressibility effect of the fluid; and implanting the phase change model that takes into account the compressibility effect of the fluid into the OpenFOAM solver to complete the calculation of the compressible phase change process in the cavitation flow. The present invention takes into account the influence of the compressibility effect of the fluid in the cavitation flow on the phase change process, better satisfies the phase change physics in actual cavitation flow, improves the accuracy of phase change calculation, and can obtain a cavitation flow field that is more in line with physical reality.

Description

Technical Field

[0001] The present invention belongs to the field of engineering computational fluid dynamics, and in particular relates to a numerical simulation method for a compressible phase change process in cavitation flow. Background Art

[0002] Cavitation is a significant and complex hydrodynamic phenomenon, widely present in hydraulic machinery, ship propulsion, and water conservancy projects. It has long been a key research focus and challenge in the field of hydrodynamics. Cavitation is essentially a vapor-liquid two-phase flow with a phase transition. This phase transition causes the fluid to exhibit strong compressibility, which in turn significantly influences the phase transition. However, conventional commercial CFD software is mostly developed based on an incompressible framework and does not consider the influence of compressibility on cavitation flows. While the open-source CFD software OpenFOAM can simulate compressible cavitation flows, the phase transition models it uses are still derived based on the incompressibility assumption. While these existing phase transition models are simple and computationally convenient, they fail to account for the influence of fluid compressibility on the phase transition process, resulting in calculated cavitation flow fields that do not fully conform to physical reality. Therefore, it is necessary to develop a numerical simulation method for compressible phase transitions in cavitation flows to further investigate the impact of compressibility on the phase transition process. Summary of the Invention

[0003] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a numerical simulation method for the compressible phase change process in cavitation flow, which takes into account the influence of the compressibility effect of the fluid in cavitation flow on the phase change process, better satisfies the phase change physics in actual cavitation flow, improves the accuracy of phase change calculation, and thus obtains a cavitation flow field that is more in line with physical reality.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] A numerical simulation method for a compressible phase change process in a cavitation flow comprises the following steps:

[0006] Step 1: Calculate the liquid density ρ in compressible flow l and liquid phase sound velocity C;

[0007] Step 2: According to the liquid density ρ l , the liquid phase sound velocity C and the Rayleigh-Plesset equation considering the compressibility of the liquid phase are used to solve the bubble wall velocity during the bubble growth or contraction process

[0008] Step 3: Based on the bubble wall velocity during bubble growth or contraction The interphase mass transfer rate is calculated by taking the material derivative of the vapor phase density inside the bubble into account, and a phase change model that takes into account the compressibility effect of the fluid is obtained;

[0009] Step 4: The phase change model considering the compressible effect of the fluid is implanted into the OpenFOAM solver to complete the calculation of the compressible phase change process in cavitation flow.

[0010] Furthermore, in step 1, the density of the liquid phase in the compressible flow is l Tait equation of state was used for calculation.

[0011]

[0012] Where p is the ambient pressure, p0 and ρ0 represent the ambient pressure and liquid density under normal working conditions, respectively. B and n are both constants, where B = 3.049 × 10 8 Pa, n = 7.15;

[0013] At the same time, considering the compressibility of the liquid phase, the calculation formula of the liquid phase sound velocity C is as follows:

[0014]

[0015] Furthermore, in step 2, the Rayleigh-Plesset equation considering the compressibility of the liquid phase is as follows,

[0016]

[0017]

[0018] Where R B is the bubble radius, P is the pressure at the bubble boundary, σ is the surface tension coefficient, and μ is the dynamic viscosity of the liquid phase, where p v (R B ) is equal to the saturated vapor pressure p sat ,

[0019] Ignoring the effects of second-order terms, surface tension, liquid viscosity, and non-condensable gases, the relationship between bubble radius change and pressure is obtained:

[0020]

[0021] Solving the above formula, we can get the bubble wall velocity during bubble growth or contraction as follows:

[0022]

[0023]

[0024] A=b 2 -3ac,B=bc-9ad (27)

[0025]

[0026]

[0027]

[0028] Furthermore, in step 3, the volume V of a single bubble B It is expressed as follows:

[0029]

[0030] Single bubble m B The quality is:

[0031] m B =ρ v V B (32)

[0032] Where, ρ v represents the vapor density inside the bubble, through the ideal state equation ρ v =p / RT, where R is the gas constant and T is the temperature, which is obtained by solving the energy equation;

[0033] The mass m of all bubbles in the cavitation area per unit volume is:

[0034] m=N B m B (33)

[0035] Where N B is the number of bubbles per unit volume;

[0036] Mass change rate per unit volume of cavitation area for:

[0037]

[0038] At the same time, the steam volume fraction α v It is expressed as follows:

[0039]

[0040] Then, the total interphase mass transfer rate caused by cavitation per unit volume is for:

[0041]

[0042] Where F is the empirical calibration coefficient, and They represent the interphase mass transfer rates of vaporization and condensation during phase change;

[0043] In the vaporization process, α nuc ×(1-α v ) instead of α v , where α nuc is the volume fraction of nucleation sites;

[0044] The phase change model considering the compressibility effect of fluid is obtained. In this model:

[0045]

[0046]

[0047] Where R B =1×10 -6 m,α nuc =5×10 -4 , F vap =50, F cond =0.01.

[0048] Furthermore, the liquid density ρ in step 1 l and the calculation formula of liquid phase sound velocity C, the bubble wall velocity during bubble growth or contraction in step 2 and the interphase mass transfer rate in step 3 Write it into a code file and compile it using wmake, then add the vapor phase density ρ to the main program of the OpenFOAM solver. v The code for solving the material derivatives is compiled using wmake, the relevant coefficients in the phase change model considering the compressible effect of the fluid are added to the phaseChangeProperties file and the model is called.

[0049] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0050] (1) The present invention provides a numerical simulation method for the compressible phase change process in cavitation flow, which takes into account the influence of the fluid compressibility effect during the phase change process and can improve the phase change simulation accuracy.

[0051] (2) The present invention provides a numerical simulation method for the compressible phase change process in cavitation flow, which can obtain a cavitation flow field that is more consistent with physical reality.

[0052] (3) The present invention provides a numerical simulation method for the compressible phase change process in cavitation flow, which can be used to quantitatively study and compare the influence of fluid compressibility on cavitation flow characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0054] Figure 1 The figure is a flow chart for implementing the numerical simulation method of the compressible phase change process in the cavitation flow.

[0055] Figure 2 Schematic diagram of the calculation example of compressible phase change around the Clark-Y hydrofoil.

[0056] Figure 3 This is the cavitation development around the Clark-Y hydrofoil at the first typical moment in the embodiment of the present invention.

[0057] Figure 4 This is the cavitation development around the Clark-Y hydrofoil at the second typical moment in the embodiment of the present invention.

[0058] Figure 5 This is the cavitation development around the Clark-Y hydrofoil at the third typical moment in the embodiment of the present invention.

[0059] Figure 6 To quantitatively compare the void volumes obtained based on experiments and traditional phase transition models.

[0060] Figure 7 The quantitative ratio is based on the void volumes obtained from experiments and examples of the present invention. DETAILED DESCRIPTION

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clearly apparent, the technical solutions in the embodiments of the present invention are fully described below in conjunction with the relevant drawings. In particular, the described embodiments are not exhaustive embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0062] In one embodiment of the present invention, Figure 2 The figure shows the computational domain for a compressible phase transition example around a Clark-Y hydrofoil. In this example, the hydrofoil chord length C = 0.07 m, the hydrofoil angle of attack is 8°, the cavitation number σ = 0.8, the spanwise width B = 0.021 m, and the upstream flow velocity U = 10 m / s.

[0063] The present invention provides a numerical simulation method for the compressible phase change process in cavitation flow, such as Figure 1 As shown, including:

[0064] Step 1: Calculate the liquid density ρ in compressible flow l and liquid phase sound velocity C;

[0065] Step 2: According to the liquid density ρ l, the liquid phase sound velocity C and the Rayleigh-Plesset equation considering the compressibility of the liquid phase are used to solve the bubble wall velocity during the bubble growth or contraction process

[0066] Step 3: Based on the bubble wall velocity during bubble growth or contraction The interphase mass transfer rate is calculated by taking the material derivative of the vapor phase density inside the bubble into account, and a phase change model that takes into account the compressibility effect of the fluid is obtained;

[0067] Step 4: The phase change model considering the compressible effect of the fluid is implanted into the OpenFOAM solver to complete the calculation of the compressible phase change process in cavitation flow.

[0068] The present invention provides a numerical simulation method for the compressible phase change process in cavitation flow, which takes into account the influence of the compressibility effect of the fluid in cavitation flow on the phase change process, better meets the phase change physics in actual cavitation flow, improves the phase change calculation accuracy, and can obtain a cavitation flow field that is more in line with physical reality.

[0069] The present invention provides a numerical simulation method for the compressible phase change process in cavitation flow, which can provide new ideas for in-depth research on the influence of the compressibility effect of fluid in cavitation flow on the phase change process.

[0070] In step 1, the liquid density ρ l The liquid phase sound velocity C is the key parameter in the compressibility calculation. By obtaining the liquid phase density ρ l and the liquid phase sound velocity C will provide support for further solving the bubble growth and contraction.

[0071] Specifically, the liquid density ρ in compressible flow l Tait equation of state was used for calculation.

[0072]

[0073] Where p is the ambient pressure, p0 and ρ0 represent the ambient pressure and liquid density under normal working conditions, respectively. B and n are both constants, where B = 3.049 × 10 8 Pa, n = 7.15;

[0074] At the same time, considering the compressibility of the liquid phase, the calculation formula of the liquid phase sound velocity C is as follows:

[0075]

[0076] Since cavitation is composed of many bubbles, the development and collapse of cavitation is closely related to the growth and contraction of bubbles. It will play a key role in phase change simulation.

[0077] In step 2, the Rayleigh-Plesset equation considering the compressibility of the liquid phase is as follows,

[0078]

[0079]

[0080] Where R B is the bubble radius, P is the pressure at the bubble boundary, σ is the surface tension coefficient, and μ is the dynamic viscosity of the liquid phase, where p v (R B ) is equal to the saturated vapor pressure p sat ,

[0081] Ignoring the effects of second-order terms, surface tension, liquid viscosity, and non-condensable gases, the relationship between bubble radius change and pressure is obtained:

[0082]

[0083] Solving the above formula, we can get the bubble wall velocity during bubble growth or contraction as follows:

[0084]

[0085]

[0086] A=b 2 -3ac,B=bc-9ad (46)

[0087]

[0088]

[0089]

[0090] In step 3, the volume of a single bubble V B It is expressed as follows:

[0091]

[0092] Single bubble m B The quality is:

[0093] m B =ρ v V B (51)

[0094] Where, ρ v represents the vapor density inside the bubble, through the ideal state equation ρ v=p / RT. Where R is the gas constant; T is the temperature, which is obtained by solving the energy equation;

[0095] The mass m of all bubbles in the cavitation area per unit volume is:

[0096] m=N B m B (52)

[0097] Where N B is the number of bubbles per unit volume.

[0098] Mass change rate per unit volume of cavitation area for:

[0099]

[0100] At the same time, the steam volume fraction α v It is expressed as follows:

[0101]

[0102] Then, the total interphase mass transfer rate caused by cavitation per unit volume is for:

[0103]

[0104] Where F is the empirical calibration coefficient, and They represent the interphase mass transfer rates of vaporization and condensation during phase change;

[0105] In order to make the model physically consistent and increase numerical stability, α is used in the vaporization process. nuc ×(1-α v ) instead of α v , where α nuc is the volume fraction of nucleation sites;

[0106] The phase change model considering the compressibility effect of fluid is obtained. In this model:

[0107]

[0108]

[0109] Where R B =1×10 -6 m,α nuc =5×10 -4 , F vap =50, F cond =0.01.

[0110] In step 4, the phase change model considering the compressible effect of the fluid is implanted into the OpenFOAM solver to complete the calculation of the compressible phase change process in cavitation flow.

[0111] Specifically, the liquid density ρ in step 1 is l and the calculation formula of liquid phase sound velocity C, the bubble wall velocity during bubble growth or contraction in step 2 and the interphase mass transfer rate in step 3 Write it into a C++ code file and compile it using wmake, then add the vapor phase density ρ to the main program of the OpenFOAM solver. v The code for solving the material derivatives is compiled using wmake. In the phaseChangeProperties file, the correlation coefficients of the phase change model considering the compressibility effect of the fluid are added, R B =1×10 -6 m,α nuc =5×10 -4 , F vap =50, F cond = 0.01 and call the model, the correlation coefficient is specifically the bubble radius R B , the volume fraction of nucleation points α nuc , Empirical calibration coefficient F during vaporization vap and the empirical calibration factor F during condensation cond .

[0112] In the embodiment of the present invention, the finite volume method is used to discretize the control equations; a high-quality hexahedral grid is used to spatially discretize the computational domain, with a total grid count of approximately 2 million. Velocity inlet and pressure outlet boundary conditions are used, and the computational domain wall is set to a no-slip boundary condition. The PISO algorithm is used for pressure and velocity coupling, and a dynamic time step is used to ensure that the maximum Courant number is less than 0.4. Figure 3-Figure 5 The figure shows the cavitation development around the Clark-Y hydrofoil at three typical moments in the embodiment of the present invention. Analysis shows that the numerical simulation method of the compressible phase transition process in cavitation flow disclosed by the present invention can accurately capture the process of cavity growth, shedding and collapse, which qualitatively demonstrates the reliability and effectiveness of the present invention. In addition, Figure 6 and Figure 7 Quantitative comparisons were made between the void volumes obtained from experiments and traditional phase transition models, as well as experiments and examples of the present invention. The analysis found that the void volume evolution calculated by the present invention agrees better with the experimental results than the traditional phase transition model, further quantitatively verifying the accuracy of the present invention's calculations.

[0113] Overall, the present invention provides a numerical simulation method for compressible phase transitions in cavitating flows. This method fully considers the impact of fluid compressibility on the phase transition process, significantly improving the accuracy of phase transition simulations and making the calculated cavitation flow field more consistent with physical reality. This invention provides a new approach for calculating compressible phase transitions in cavitating flows.

[0114] The present invention discloses a numerical simulation method for the compressible phase change process in cavitation flow, which is applied to the field of numerical simulation of cavitation hydrodynamics, and is particularly used to study the influence of the compressibility effect of the fluid in cavitation flow on the phase change process. It helps to deeply reveal the physical mechanism of compressible cavitation flow and can be applied to related engineering fields to solve practical problems.

[0115] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A numerical simulation method for compressible phase change process in cavitation flow, characterized in that: The following steps are involved: Step 1: Calculate the liquid density in compressible flow and liquid phase sound velocity C ; Wherein, in step 1, the density of the liquid phase in the compressible flow Tait equation of state was used for calculation. (1) Where, For environmental pressure, and represent the ambient pressure and liquid density under normal working conditions, respectively. B and n are all constants, among which, , n=7.15; At the same time, considering the compressibility of the liquid phase, the liquid phase sound velocity The calculation formula is as follows: (2) Step 2: According to the liquid density , liquid phase sound velocity C The Rayleigh-Plesset equation considering the compressibility of the liquid phase is used to solve the bubble wall velocity during the bubble growth or contraction process. ; In step 2, the Rayleigh-Plesset equation considering the compressibility of the liquid phase is as follows, (3) (4) Where, is the bubble radius, is the pressure at the bubble boundary, is the surface tension coefficient, is the dynamic viscosity of the liquid phase, where Equal to saturated vapor pressure , , ; Ignoring the effects of second-order terms, surface tension, liquid viscosity, and non-condensable gases, the relationship between bubble radius change and pressure is obtained: (5) Solving the above formula, we can get the bubble wall velocity during bubble growth or contraction ,as follows: (6) (7) (8) (9) (10) (11) Step 3: Based on the bubble wall velocity during bubble growth or contraction The interphase mass transfer rate is calculated by taking the material derivative of the vapor phase density inside the bubble into account, and a phase change model that takes into account the compressibility effect of the fluid is obtained; Step 4: The phase change model considering the compressible effect of the fluid is implanted into the OpenFOAM solver to complete the calculation of the compressible phase change process in cavitation flow.

2. The numerical simulation method for compressible phase change in cavitation flow according to claim 1, characterized in that: In step 3, the volume of a single bubble It is expressed as follows: (12) Single bubble The quality is: (13) Where, The vapor density inside the bubble is expressed by the ideal state equation Solve to get, where, R is the gas constant; T is the temperature, obtained by solving the energy equation; The mass of all bubbles in the cavitation area per unit volume for: (14) Where, is the number of bubbles per unit volume; Mass change rate per unit volume of cavitation area for: (15) At the same time, the steam volume fraction It is expressed as follows: (16) Then, the total interphase mass transfer rate caused by cavitation per unit volume is for: (17) Where, F is the empirical calibration coefficient, and They represent the interphase mass transfer rates of vaporization and condensation during phase change; In the vaporization process to replace ,in is the volume fraction of nucleation sites; The phase change model considering the compressibility effect of fluid is obtained. In this model: (18) (19) Where, , , , .

3. The numerical simulation method for compressible phase change in cavitation flow according to claim 2, characterized in that: The density of the liquid phase in step 1 and liquid phase sound velocity C The calculation formula of the bubble wall velocity in the bubble growth or contraction process in step 2 is and the interphase mass transfer rate in step 3 Write it into a code file and compile it using wmake to add vapor phase density to the main program of OpenFOAM solver The code for solving the material derivatives is compiled using wmake, the relevant coefficients in the phase change model considering the compressible effect of the fluid are added to the phaseChangeProperties file and the model is called.

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