A method for numerical prediction of cavitation in sodium chloride solutions

Abstract

This invention discloses a numerical prediction method for cavitation in sodium chloride solution, belonging to the field of computational fluid dynamics. The method optimizes the numerical simulation results by modifying the empirical coefficients and medium properties in the Zwart cavitation model and comparing them with experimental results. The steps include: describing the medium properties of the sodium chloride solution by introducing mass fraction w% and solution temperature T; establishing the relationship between the density ρ of the sodium chloride solution and mass fraction w% and temperature T; establishing the relationship between the viscosity μ of the sodium chloride solution and mass fraction w% and temperature T; and establishing the saturated vapor pressure p of the sodium chloride solution. s The relationship between sodium chloride solution mass fraction (w%) and temperature (T) is investigated. Finally, the Zwart cavitation model under the influence of sodium chloride solution mass fraction (w%) and temperature (T) is incorporated into the cavitation flow solver to simulate the effect of sodium chloride solution on cavitation characteristics. This invention can significantly improve the accuracy of cavitation prediction in sodium chloride solution.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of engineering computational fluid mechanics, and particularly relates to a cavitation numerical prediction method in sodium chloride solution. BACKGROUND

[0002] In the field of biochemistry, cavitation effect is often used to degrade organic matter in water. Hydrodynamic cavitation has the ability to oxidize organic matter and has low operating cost. At the same time, hydrodynamic cavitation has the advantages of simple structure, low manufacturing cost, less pollution, no by-products, and is suitable for large-scale application.

[0003] In the prior art, hydrodynamic cavitation can be combined with other pretreatment methods such as alkaline reaction to improve the process efficiency, so that the solution contains a large amount of ions instead of ordinary water solution. In addition, in saline-alkali areas, Venturi sprinkling irrigation devices are used for crop irrigation, and high-speed jets can cause cavitation, and the medium also contains a large amount of ions. Therefore, it is particularly important to predict the flow through numerical simulation to improve the performance of the hydrodynamic cavitation device.

[0004] The existing numerical simulation method of hydrodynamic mechanical cavitation flow has the following disadvantages: the influence of ion-containing medium in the solution cannot be considered, resulting in inaccurate prediction of the cavitation performance of ion-containing medium, and there is a lack of effective numerical prediction method. Therefore, in view of the deficiencies of the numerical simulation method for predicting cavitation flow of ion-containing medium, it is necessary to develop and improve a numerical calculation method which can reasonably predict the cavitation characteristics of ion-containing solution. The present application selects NaCl solution which is the most common medium in the medium, rich in Na + and Cl - ions, i.e. seawater medium. SUMMARY

[0005] The purpose of the present application is to provide a cavitation numerical prediction method in sodium chloride solution, which can consider the medium properties of the fluid and simulate the influence of sodium chloride solution on cavitation characteristics.

[0006] The technical scheme of the present application is: a cavitation numerical prediction method in sodium chloride solution, comprising the following steps:

[0007] Step 1: Introducing mass fraction w% and solution temperature T to describe the medium properties of sodium chloride solution;

[0008] Step 2: Creating the relationship between the density p of sodium chloride solution and the mass fraction w% and temperature T;

[0009] Step 3: Creating the relationship between the viscosity p of sodium chloride solution and the mass fraction w% and temperature T;

[0010] Step 4: Creating the relationship between the saturated vapor pressure p srelationship between mass fraction w% and temperature T;

[0011] Step five: implant cavitation model under the influence of mass fraction w% and temperature T of sodium chloride solution into cavitation flow solver;

[0012] The definition of mass fraction w% of solution in step one is the ratio of mass of solute sodium chloride to the mass of sodium chloride solution dissolved in water, and mass fraction w% does not exceed the maximum solubility of sodium chloride in water, and the temperature of sodium chloride solution is in Celsius (℃).

[0013] The density ρ in step two satisfies the following formula with mass fraction w% and temperature T:

[0014] ρ = 1003.2 + 7.5w - 0.4T (1)

[0015] The viscosity μ in step three satisfies the following formula with mass fraction w% and temperature T:

[0016] μ = (0.1w 2 +w - 3.3T + 175.5) × 10 -5 (2)

[0017] The saturated vapor pressure p s in step four satisfies the following formula with mass fraction w% and temperature T:

[0018] p s = -22w + 126T + 157 (3)

[0019] The cavitation flow solver in step five is based on Zwart cavitation model, whose control equation describes the mass transfer between vapor and liquid phases, satisfying the following expression:

[0020]

[0021] In the formula, p represents the pressure in the flow field, p s represents the critical pressure of liquid medium to vapor phase, and represent the evaporation rate and condensation rate between vapor and liquid phases, F vap and F cond represent the evaporation coefficient and condensation coefficient, α v and ρ v represent the volume fraction and density of vapor phase, ρ represents the density of liquid medium, R nuc and α nuc represent the radius and volume fraction of gas nucleus.

[0022] In the evaporation term of Zwart cavitation model in step five, the influence of solution mass fraction is introduced, and the evaporation coefficient is corrected, satisfying the following expression:

[0023] F vap-m =F vap +4w (5)

[0024] The correction value F for the evaporation coefficient in the above formula vap-m Replace F in formula (4) vap The position is written into the control equations of the original Zwart cavitation model by writing expressions.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention introduces the mass fraction and temperature of sodium chloride solution into the numerical prediction of cavitation flow, which more fully considers the influence of the physical properties of the fluid medium on cavitation; and can effectively improve the accuracy of numerical prediction of cavitation in sodium chloride solution. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the implementation of a numerical prediction method for cavitation in sodium chloride solution according to the present invention.

[0027] Figure 2 This is a schematic diagram of a cavitation flow example inside a Venturi tube.

[0028] Figure 3 A comparison chart showing the calculation results of the cavitation region inside the Venturi tube.

[0029] The structure consists of 1 inlet cylindrical section, 2 conical contraction section, 3 cylindrical throat section, 4 conical diffusion section, and 5 outlet cylindrical section. Detailed Implementation

[0030] To better illustrate the purpose and advantages of the present invention, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0031] The Venturi tube, as one of the simplest cavitation generators in industry, has many advantages. Venturi tube experimental platforms are relatively inexpensive, have a simple system, occupy a small area, and produce low noise in the experimental environment. While ensuring structural rigidity and hardness requirements, they can be made of transparent acrylic glass, allowing for high-speed photography to facilitate comparison of cavitation cavity lengths between experiments and numerical simulations, thus verifying the accuracy of the prediction method. Therefore, the Venturi tube is used as the object of simulation and experimentation. The described embodiments are not all embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] like Figure 2As shown in Fig. 1, it is a schematic diagram of the calculation domain of the cavitation flow calculation example in a Venturi tube, which includes an inlet cylinder segment 1, a conical contraction segment 2, a cylinder throat segment 3, a conical diffusion segment 4 and an outlet cylinder segment 5 arranged in sequence. The diameter D of the cylinder throat segment 3 and the length L of the cylinder throat segment 3 are both 8 mm. The front contraction angle α of the throat segment is 41°, and the rear diffusion angle β of the throat segment is 12°. The diameters of the inlet and outlet cylinder segments of the Venturi tube are both 4.25D. The total length of the Venturi tube is 33.5L. The set flow velocity V0 is 0.92 m / s.

[0033] As shown in Fig. 2, it is a flow chart of a cavitation numerical prediction method for a sodium chloride solution. The specific implementation steps are as follows: Figure 1 As shown in Fig. 2, it is a flow chart of a cavitation numerical prediction method for a sodium chloride solution. The specific implementation steps are as follows:

[0034] Step one: Introduce the mass fraction w% and the solution temperature T to describe the medium properties of the sodium chloride solution.

[0035] The definition of the mass fraction w% of the solution is the ratio of the mass of the solute sodium chloride to the mass of the sodium chloride solution dissolved in water, and the mass fraction w% does not exceed the maximum solubility of sodium chloride in water. The temperature of the sodium chloride solution is the temperature of the inlet flow medium of the Venturi tube, and the unit of the temperature of the sodium chloride solution is Celsius (℃).

[0036] Step two: Create the relationship between the density p of the sodium chloride solution and the mass fraction w% and the temperature T, which satisfies the following formula:

[0037] p = 1003.2 + 7.5w - 0.4T (1)

[0038] The calculation result of the solution density (unit: kg / m3) is transmitted to the flow control equation of the numerical simulation calculation, that is, it is written into the computational fluid dynamics simulation software in the form of an expression, which is used to represent the density of the liquid medium.

[0039] Step three: Create the relationship between the viscosity p of the sodium chloride solution and the mass fraction w% and the temperature T, which satisfies the following formula:

[0040] p = (0.1w 2 +w - 3.3T + 175.5) x 10 -5 (2)

[0041] The calculation result of the solution viscosity (unit: Pa·s) is transmitted to the flow control equation of the numerical simulation calculation, that is, it is written into the computational fluid dynamics simulation software in the form of an expression, which is used to represent the dynamic viscosity of the liquid medium.

[0042] Step four: Create the relationship between the saturated vapor pressure p s of the sodium chloride solution and the mass fraction w% and the temperature T, which satisfies the following formula:

[0043] ps = -22w + 126T + 157 (3)

[0044] The calculated results of the solution saturation vapor pressure (unit: Pa) are passed to the cavitation flow control equation of the numerical simulation calculation, that is, written into the computational fluid dynamics simulation software by writing expressions, to represent the critical pressure of the liquid medium to the vapor phase.

[0045] Step five: implant the cavitation model under the influence of the mass fraction w% and temperature T of the sodium chloride solution into the cavitation flow solver, based on the Zwart cavitation model, whose control equation describes the mass transfer between the vapor and liquid phases, satisfying the following expression:

[0046]

[0047] In the formula, p represents the pressure in the flow field, p s represents the critical pressure of the liquid medium to the vapor phase, and in the flow simulation calculation, the mass transfer between the vapor and liquid phases is determined by comparing the size relationship between p and p s ; and represent the evaporation rate and condensation rate between the vapor and liquid phases, F vap and F cond represent the evaporation coefficient and condensation coefficient, and the general empirical values are F vap = 50 and F cond = 0.01, α v and ρ v represent the volume fraction and density of the vapor phase, ρ represents the density of the liquid medium, R nuc and α nuc represent the radius and volume fraction of the gas nucleus, respectively satisfying the general empirical values R nuc = 1 × 10 -6 m and α nuc = 5 × 10 -4 .

[0048] The influence of the solution mass fraction is introduced into the evaporation term of the Zwart cavitation model, and the evaporation coefficient is corrected to satisfy the following expression:

[0049] F vap-m = F vap + 4w (5)

[0050] The corrected value F vap-m of the evaporation coefficient in the above formula is replaced into the position of F vap in formula (4), and written into the control equation of the original Zwart cavitation model by writing expressions.

[0051] In the embodiment, the flow control equation is discretized by using the finite volume method; the calculation domain of the Venturi tube is spatially discretized by using a hexahedral structure grid, which meets the grid-independent verification requirement; a boundary condition of flow inlet and pressure outlet is used; and the convergence precision RMS=10 -5 .

[0052] As shown in Figure 3 , the deviation of the cavitation region predicted by using the prediction method of the application from the experiment is compared, and compared with the analysis of the calculation result of the traditional cavitation model, it is found that the application has the advantages that: the mass fraction and temperature of the sodium chloride solution are introduced in the numerical prediction of the cavitation flow, and the influence of the physical properties of the fluid medium on the cavitation is more fully considered; and the numerical prediction method of the cavitation in the sodium chloride solution can significantly improve the prediction precision of the cavitation in the sodium chloride solution.

[0053] The application is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the application, those skilled in the art can make some substitutions and deformations to some technical features according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the application.

Claims

1. A numerical prediction method for cavitation in sodium chloride solution, characterized in that, Includes the following steps: Step 1: Introduce the mass fraction w% and solution temperature T to describe the medium properties of the sodium chloride solution; Step 2: Establish the relationship between the density ρ of the sodium chloride solution and its mass fraction w% and temperature T; Step 3: Establish the relationship between the viscosity μ of the sodium chloride solution and its mass fraction w% and temperature T; Step 4: Establish the saturated vapor pressure p of the sodium chloride solution s Relationship between mass fraction w% and temperature T; Step 5: Incorporate the cavitation model under the influence of sodium chloride solution mass fraction w% and temperature T into the cavitation flow solver; The mass fraction w% of the solution mentioned in step one is defined as the ratio of the mass of sodium chloride solute to the mass of sodium chloride solution dissolved in water, and the mass fraction w% does not exceed the maximum solubility of sodium chloride in water. The unit of temperature of sodium chloride solution is degrees Celsius (°C). The cavitation flow solver described in step five is based on the Zwart cavitation model, whose governing equations describe the mass transfer between the vapor and liquid phases and satisfy the following expression: In the formula, p represents the pressure in the flow field, p s This represents the critical pressure at which a liquid medium transitions to the vapor phase. and F represents the evaporation rate and condensation rate between the vapor and liquid phases. vap and F cond α represents the evaporation coefficient and condensation coefficient. v and ρ v R represents the volume fraction and density of the vapor phase, ρ represents the density of the liquid medium, and R represents the density of the vapor phase. nuc and α nuc This indicates the radius and volume fraction of the gas nucleus.

2. The method for numerical prediction of cavitation in sodium chloride solution according to claim 1, characterized in that, The density ρ, mass fraction w%, and temperature T mentioned in step two satisfy the following formula: ρ = 1003.2 + 7.5w - 0.4T.

3. The method for numerical prediction of cavitation in sodium chloride solution according to claim 1, characterized in that, The viscosity μ, mass fraction w%, and temperature T mentioned in step three satisfy the following formula: μ=(0.1w 2 +w-3.3T+175.5)×10 -5 。 4. The numerical prediction method for cavitation in sodium chloride solution according to claim 1, characterized in that, The saturated vapor pressure p mentioned in step four s The mass fraction w% and temperature T satisfy the following formula: p s =-22w+126T+157。 5. The numerical prediction method for cavitation in sodium chloride solution according to claim 1, characterized in that, The influence of solution mass fraction is introduced into the evaporation term of the Zwart cavitation model described in step five, and the evaporation coefficient is corrected to satisfy the following expression: F vap-m =F vap +4w The correction value F for the evaporation coefficient in the above formula vap-m Replace with F vap The position is written into the control equations of the original Zwart cavitation model by writing expressions.

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