A cavitation model modification method considering transient effects of flow field

Abstract

The present invention discloses a method for correcting a cavitation model that takes into account the transient effects of a flow field. The method comprises simulating the change of the bubble radius using the Rayleigh-Plesset equation, performing a magnitude analysis based on cavitation influencing factors to obtain a nonlinear bubble motion equation; integrating the nonlinear bubble motion equation to obtain a bubble wall velocity model that takes into account the transient effects of the flow field, using the bubble wall velocity model to obtain a mass transfer rate function that takes into account the transient effects of the flow field, and finally correcting the mass transfer rate of the original cavitation model based on the mass transfer rate function that takes into account the transient effects of the flow field, thereby achieving correction of the cavitation model. The corrected cavitation model provided by the present invention fully takes into account the influence of the transient effects of the fluid on the cavitation flow, improves the accuracy of phase change simulation, and makes the calculated cavitation flow field more consistent with physical reality. The method of the present invention provides a new idea for calculating transient changes in cavitation flow.

Description

Technical Field

[0001] The invention belongs to the technical field of computational fluid dynamics, and particularly relates to a cavitation model correction method considering transient effects of flow fields. Background Art

[0002] Cavitation is the phase transition from liquid to vapor in a localized region of a fluid when the ambient pressure falls below the fluid's saturated vapor pressure. It is an important and complex hydrodynamic phenomenon, widely present in hydraulic machinery, ship propulsion systems, and water conservancy projects. It has long been a key and challenging area of ​​research in hydrodynamics. For example, it can cause material erosion and reduced mechanical efficiency on the surfaces of underwater propellers and other hydraulic machinery, as well as cavitation damage in flow-passing components. The unique unsteady and transient nature of cavitation makes its experimental study challenging. With advances in computer performance, numerical simulations can provide more detailed flow field characteristics, and its application in the field of cavitation is becoming increasingly widespread.

[0003] The transient characteristics of cavitation can cause problems such as hydraulic machinery vibration, increased hydrodynamic force, increased pressure pulsation, noise, and surface erosion. However, there is currently no unique CFD method that can solve the transient cavitation problem. Therefore, it is necessary to develop a cavitation kinematic simulation method that takes into account the transient effects of the flow field to deeply study the influence of the transient effects of cavitation on the cavitating flow field and accurately simulate more flow field details of the real cavitation flow, which is of great significance for improving the performance of hydraulic machinery using cavitation flow numerical simulation technology. Summary of the Invention

[0004] In order to solve the problems existing in the background technology, the purpose of the present invention is to provide a cavitation model correction method that considers the transient effects of the flow field, takes the transient effects of the flow field in the cavitation flow into account, improves the calculation accuracy, and thus obtains a cavitation flow field that is more in line with physical reality.

[0005] The technical solution adopted by the present invention is as follows, comprising the following steps:

[0006] Step S1: First, a cavitation model of a water conservancy machinery basin is established in a computer. A processor in the computer obtains a nonlinear bubble motion equation of the cavitation model based on the change of the bubble radius of the cavitation model;

[0007] Step S2: Next, the processor obtains a bubble wall velocity model that takes into account the transient effect of the flow field according to the nonlinear bubble motion equation;

[0008] Step S3: Then, the processor obtains a mass transfer rate function that takes into account the transient effect of the flow field based on the bubble wall velocity model;

[0009] Step S4. Finally, the processor modifies the mass transfer rate of the original cavitation model based on the mass transfer rate function considering the transient effect of the flow field, that is, the cavitation model is modified, and the cavitation phenomenon in the water conservancy machinery basin is predicted according to the modified cavitation model.

[0010] Step S5: Compare the cavitation calculation results based on the cavitation model considering transient effects with the published test results, and compare the numerical model of hydrofoil cavitation flow based on the comparison results, thereby verifying that a modified cavitation model considering the transient effects of the flow field is more accurate than the traditional cavitation model, specifically including:

[0011] The preset hydrofoil cavitation flow field is meshed, boundary conditions are set, the COUPLED algorithm is used to solve the pressure-velocity coupling equation, the least squares grid format is used to solve the discrete equations in space, the PRESTO algorithm is used to solve the pressure gradient equation, the bounded central difference format is used to solve the momentum equation, the bounded second-order implicit method is used to solve the transient equation, and the DES kw turbulence model is used to solve the Reynolds equation to calculate turbulent flow. The cavitation model considering transient effects is used to realize the gas-liquid phase change process.

[0012] In step S1, the nonlinear bubble motion equation of the cavitation model is obtained by processing according to the following formula:

[0013]

[0014] In the above formula, P v Indicates the internal pressure of the bubble; P t represents the ambient pressure at time t; ρ l represents the density of the liquid outside the cavitation bubble; R represents the radius of the cavitation bubble; It means to find the first derivative of the cavitation radius R with respect to the time variable t; It means to take the second derivative of the cavitation radius R with respect to the time variable t.

[0015] In step S2, the bubble wall velocity model considering the transient effect of the flow field is obtained according to the following formula:

[0016]

[0017] in, represents the derivative of the cavitation radius with respect to the time variable t; ρ l represents the density of the liquid outside the cavitation bubble; P v represents the internal pressure of the bubble; P0 represents the ambient pressure at the initial moment of a time step; P t represents the ambient pressure at the end of a time step, C0 is the preset model coefficient; R0 represents the initial radius of the cavitation nucleus.

[0018] In step S3, the mass transfer rate function considering the transient effect of the flow field is obtained according to the following formula:

[0019]

[0020]

[0021] in, represents the mass transfer rate considering the transient effect of the flow field; α represents the bubble volume fraction per unit volume; ρ v represents the gas density; i represents the state parameter, i∈{1,2}, when the cavitation is in the condensation process, i is 1, when the cavitation is in the evaporation process, i is 2, R B represents a given constant term; ρ l represents the density of the liquid outside the cavitation bubble; P v represents the internal pressure of the bubble; P0 represents the ambient pressure at the initial moment of a time step; P t represents the ambient pressure at the end of a time step, C0 is the preset model coefficient; R0 represents the initial radius of the cavitation nucleus; R represents the cavitation radius; and n represents the bubble number density.

[0022] The expression of the modified cavitation model is as follows:

[0023]

[0024] Among them, Re represents the mass transfer rate of the cavitation evaporation process; Rc represents the mass transfer rate of the cavitation condensation process; F vap Indicates the evaporation process coefficient; F cond represents the condensation process coefficient; α nuc represents the volume fraction of nucleation points; α represents the volume fraction of bubbles per unit volume; R B represents a given constant term; || represents the absolute value function; ρ v Indicates the gas density.

[0025] The original cavitation model includes a mass transfer model based on the Rayleigh-Plesset equation that ignores gravity, surface tension, and viscous forces. The modified cavitation model uses a nonlinear cavitation model derived from the Rayleigh-Plesset equation that considers the second-order derivative of the radius, while also taking into account the transient effect of ambient pressure.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. The present invention adopts a cavitation model correction method that considers the transient effects of the flow field and proposes a nonlinear cavitation model that considers the transient effects of the flow field. The corrected cavitation model fully considers the influence of the transient effects of the fluid on the cavitation flow, improves the phase change simulation accuracy, and makes the calculated cavitation flow field more consistent with physical reality. This method provides a new idea for the calculation of transient changes in cavitation flow.

[0028] 2. The present invention provides a nonlinear cavitation model that takes into account the transient effect of the flow field. The ratio of the initial radius of the cavitation core to the radius of the cavitation bubble in the model is The second-order derivative of the bubble radius is reflected in the calculation process, and the transient effect of the ambient pressure is considered in the calculation process, and the pressure at the initial and final states of each time step Δt is regarded as P0 and P t , considering the transient effect of ambient pressure, the new cavitation model can improve the computational accuracy of simulating the periodic cavitation evolution on the hydrofoil surface, and provide reliable flow field parameters such as pressure and cavitation volume fraction for cavitation flow calculation.

[0029] 3. The present invention provides a cavitation model correction method that takes into account the transient effects of the flow field, and proposes a nonlinear cavitation model that takes into account the transient effects of the flow field. It can be used to quantitatively study and compare the influence of the transient effects of the fluid flow field on the cavitation flow characteristics, and provide a theoretical basis for the unsteady cavitation flow of hydraulic machinery. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0031] Figure 1 A flowchart for implementing the numerical simulation method of the compressible phase change process in the cavitation flow;

[0032] Figure 2 Schematic diagram of the calculation domain of the cavitation flow field of the hydrofoil according to an embodiment of the present invention;

[0033] Figure 3 Schematic diagram of the computational domain grid of the hydrofoil cavitation flow field according to an embodiment of the present invention;

[0034] Figure 4 Schematic diagram comparing the calculation and experimental results of the periodic cavitation growth process of the hydrofoil according to an embodiment of the present invention;

[0035] Figure 5 Schematic diagram comparing lift performance under different cavitation numbers obtained based on experiments and traditional cavitation models, and based on experiments and embodiments of the present invention; DETAILED DESCRIPTION

[0036] The present invention is described in detail below with reference to specific implementation cases. The following implementation cases will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form.

[0037] In one embodiment of the present invention, a Figure 2 The following is a schematic diagram of the computational domain for a NACA66-2d hydrofoil considering the transient effects of cavitation flow. In this example, the hydrofoil chord length C = 150 mm, the hydrofoil angle of attack is 6°, the domain length is 8 times the chord length (8C), the leading edge is located 2C from the computational domain inlet, and the trailing edge is located 5C from the exit. The computational domain is meshed, and the mesh diagram is shown in the figure below. Figure 3 As shown, the computational domain inlet and outlet, solid wall, and mesh number are defined at the same time. The boundary layer is selected to ensure that y+<5, where y is the first mesh thickness from the hydrofoil wall. A structured mesh is used, and meshes are refined in the leading and trailing edge regions of the hydrofoil.

[0038] The present invention provides a cavitation model correction method considering the transient effect of flow field, such as Figure 1 As shown, the following steps are included:

[0039] Step S1: First, a cavitation model of a hydraulic machinery basin is established in a computer. The Rayleigh-Plesset equation is used to simulate the change of the cavitation radius under spherically symmetric acoustic pressure driving conditions. The processor in the computer performs a magnitude analysis based on cavitation influencing factors to obtain a nonlinear bubble motion equation.

[0040] Step S2: Considering the unsteadiness of pressure, the processor integrates the nonlinear bubble motion equation to obtain a bubble wall velocity model that considers the transient effect of the flow field, and models the integral term of the pressure derivative to ensure that the modified model is compatible with the original model;

[0041] In step S3, the processor calculates the interphase mass transfer rate according to the bubble wall velocity model to obtain a revised cavitation model, and subsequently predicts the cavitation phenomenon in the watershed of the hydraulic machinery according to the revised cavitation model.

[0042] Step S4: Compare the cavitation calculation results based on the consideration of transient effects with the published test results, and compare the numerical model of the hydrofoil cavitation flow based on the comparison results, thereby verifying that a modified cavitation model and flow field prediction method that considers the transient effects of the flow field are more accurate than the traditional cavitation model simulation method.

[0043] The specific steps for obtaining the nonlinear bubble motion equation in step S1 are as follows:

[0044] Step S1.1: Perform a dimensional analysis of the cavitation under spherically symmetric acoustic pressure driving conditions. Ignoring factors such as gravity, surface tension, viscous forces, and non-spherical shape, the ordinary differential equation for the bubble in pure radial motion is the Rayleigh-Plesset equation, as shown in Formula 1:

[0045]

[0046] Where R is the bubble radius; t is the time variable; ρ l Indicates liquid density; P g Indicates the non-condensable gas pressure; P a (t) represents the driving sound pressure; P w Indicates the ambient pressure of the liquid outer boundary, which is equal to the standard atmospheric pressure; c l represents the speed of sound in the liquid. In a specific embodiment, P w =1atm,ρ l =10 3 kg / m 3 , c l =1480m / s.

[0047] The left side of the above formula 1 is the second-order derivative and first-order derivative of the cavitation radius, and the right side is the pressure term and the first-order derivative of the pressure. Given the initial cavitation radius length and the driving sound pressure form, the fourth-order Runge-Kutta method can be used to directly solve formula 1. Assuming that the cavitation nucleus with an initial cavitation radius of R0 is in the low-pressure area at time 0, a typical solution for the cavitation radius when flowing through the low-pressure area can be obtained.

[0048] Step S1.2: Based on the cavitation radius solution obtained in step S1.1, the magnitude analysis of the two cavitation radius derivative terms, the pressure term, and the pressure derivative term in formula 1 can be performed. These four terms are all functions of the cavitation radius. The non-condensable gas pressure can be expressed using formula 2 containing the cavitation radius:

[0049]

[0050] Among them, P g (R,t) represents the non-condensable gas pressure at time t when the cavitation radius is R; σ represents the surface tension coefficient; R0 represents the initial radius of the cavitation nucleus; a represents the gas van der Waals exclusion radius, usually a = R0 / 8.5; γ represents the adiabatic constant, usually γ = 1;

[0051] Through the magnitude analysis, we can see that the magnitude of the radius first-order derivative term and the pressure term is 10 2 , the second-order derivative of the radius is of order 10 1 , the first-order derivative of pressure is of order 10 0 , so after ignoring the first-order derivative of pressure, the Rayleigh-Plesset equation can be simplified to Formula 3:

[0052]

[0053] The above formula is the simplified nonlinear bubble motion equation, P vIndicates the internal pressure of cavitation bubbles; P t represents the ambient pressure at time t, ρ l represents the density of the liquid outside the cavitation bubble; R represents the radius of the cavitation bubble; It means to find the first derivative of the cavitation radius R with respect to the time variable t; It means to find the second derivative of the cavitation radius R with respect to the time variable t;

[0054] In step S2, a bubble wall velocity model considering the transient effect of the flow field is obtained, and the pressure derivative integral term is modeled. The specific steps are as follows:

[0055] Step S2.1: Multiply both the left and right sides of Formula 3 by

[0056] According to the initial condition at time zero t = 0 Integrating both sides of the equation with respect to time yields the first-order derivative expression of the cavitation radius, Formula 4:

[0057]

[0058] Among them, P0 represents the ambient pressure at the initial moment within a time step; P t Indicates the ambient pressure at the end of a time step, P0 and P t They represent the ambient pressure at the beginning and end of the time step in the time interval △t, respectively. The subscript 0 represents the value calculated at the end of the previous time step, and the subscript t represents the value calculated at the end of the current time step. The pressure derivative integral term of the last item on the right side of Formula 4 reflects the factors affecting the pressure change within a time step.

[0059] Step S2.2: Modify the pressure derivative integral term in Formula 4. Formula 5 is used to express the pressure derivative integral term:

[0060]

[0061] Among them, C0 is the preset model coefficient;

[0062] Using Formula 5 to replace the pressure derivative integral term in Formula 4, the rate of change of the cavitation radius is Finally, it is expressed by formula 6:

[0063]

[0064] In step S3, the interphase mass transfer rate is calculated using the bubble wall velocity model to obtain a modified cavitation model. The specific steps include:

[0065] Step S3.1: Use Formula 7 to characterize the change in bubble radius during evaporation and condensation of cavitation bubbles:

[0066]

[0067] Where i represents the state parameter, i∈{1,2}, i=1 represents the condensation process; when i=2 represents the evaporation process;

[0068] Step S3.2: Use Formula 8 to obtain the mass change rate of a single bubble in the cavitation region:

[0069]

[0070] Where m represents the mass of a single bubble; ρ v Indicates gas density;

[0071] Assuming the bubble number density is n, the total mass transfer rate within a unit volume can be obtained using Formula 9:

[0072]

[0073] in, is the mass transfer rate per unit volume.

[0074] Next, the gas volume fraction of bubbles per unit volume is obtained using Formula 10:

[0075]

[0076] Where α represents the bubble volume fraction within one calculation unit;

[0077] Combined with Formula 9, the mass transfer rate can also be expressed by Formula 11:

[0078]

[0079] Among them, R B represents the constant term, which is 10 -6 m.

[0080] Substituting Formula 7 into Formula 11, we can obtain the mass transfer rate equation considering the transient effect of the flow field, as shown in Formula 12:

[0081]

[0082] Step S3.3: Introduce the empirical calibration coefficient and refine the mass transfer rate equation into the corrected cavitation model obtained by the evaporation process and the condensation process, as shown in Formula 13:

[0083]

[0084] Among them, R e and R c are the mass transfer rates of the bubble evaporation process and the condensation process respectively; Fvap Indicates the evaporation process coefficient, which can be taken as 50; F cond Indicates the condensation process coefficient, which can be 0.01, α nuc represents the volume fraction of nucleation points, which can be taken as 5×10 -4 ; R B represents the constant term, which is 10 -6 m.

[0085] In step S4, the calculation results of the cavitation model considering transient effects are compared with the published test results, including:

[0086] The flow parameters are shown in Table 1:

[0087] Table 1 Flow condition parameters

[0088]

[0089] The COUPLED algorithm is used to solve the pressure-velocity coupling equation, the least squares grid format is used to solve the spatial discrete equation, the PRESTO algorithm is used to solve the pressure gradient equation, the bounded central difference format is used to solve the momentum equation, the bounded second-order implicit method is used to solve the transient equation, and the DES kw turbulence model is used to solve the Reynolds equation to calculate turbulent flow. The cavitation model considering transient effects is used to realize the gas-liquid phase change process.

[0090] Additionally, in one embodiment, Figure 4 As shown in the figure, the periodic cavitation growth process of the hydrofoil obtained based on the experiment and the embodiment of the present invention is compared. It can be seen from the analysis that the modified cavitation model and flow field prediction method considering the transient effect of the flow field disclosed in the present invention can accurately capture the process of cavity growth, shedding and collapse, which qualitatively illustrates the reliability and effectiveness of the present invention.

[0091] Additionally, in one embodiment, Figure 5 As shown, a quantitative comparison of lift performance at different cavitation numbers obtained based on experimental and traditional cavitation models, as well as experimental and embodiments of the present invention, is presented. The analysis found that the cavity volume evolution calculated by the present invention is in better agreement with experimental results than the traditional phase change model.

[0092] In summary, the modified cavitation model proposed by the present invention, which accounts for transient effects in the flow field, fully considers the impact of fluid transients on cavitation flows, improves the accuracy of phase change simulations, and makes the calculated cavitation flow field more consistent with physical reality. This invention provides new insights into the calculation of transient changes in cavitation flows.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A cavitation model correction method considering the transient effect of flow field, characterized in that: The following steps are involved: Step S1: First, a cavitation model of a water conservancy machinery basin is established in a computer. A processor in the computer obtains a nonlinear bubble motion equation of the cavitation model based on the change of the bubble radius of the cavitation model; Step S2: Next, the processor obtains a bubble wall velocity model that takes into account the transient effect of the flow field according to the nonlinear bubble motion equation; Step S3: Then, the processor obtains a mass transfer rate function that takes into account the transient effect of the flow field based on the bubble wall velocity model; Step S4: Finally, the processor modifies the mass transfer rate of the original cavitation model based on the mass transfer rate function that considers the transient effect of the flow field, that is, the cavitation model is modified, and the cavitation phenomenon in the watershed of the hydraulic machinery is predicted based on the modified cavitation model; In step S1, the nonlinear bubble motion equation of the cavitation model is obtained by processing according to the following formula: In the above formula, P v Indicates the internal pressure of the bubble; P t represents the ambient pressure at time t; ρ l represents the density of the liquid outside the cavitation bubble; R represents the radius of the cavitation bubble; It means to find the first derivative of the cavitation radius R with respect to the time variable t; It means to find the second derivative of the cavitation radius R with respect to the time variable t; In step S2, the bubble wall velocity model considering the transient effect of the flow field is obtained according to the following formula: in, represents the derivative of the cavitation radius with respect to the time variable t; ρ l represents the density of the liquid outside the cavitation bubble; P v represents the internal pressure of the bubble; P0 represents the ambient pressure at the initial moment of a time step; P t represents the ambient pressure at the end of a time step, C0 is the preset model coefficient; R0 represents the initial radius of the cavitation nucleus; In step S3, the mass transfer rate function considering the transient effect of the flow field is obtained according to the following formula: in, represents the mass transfer rate considering the transient effect of the flow field; α represents the bubble volume fraction per unit volume; ρ v represents the gas density; i represents the state parameter, i∈{1,2}, when the cavitation is in the condensation process, i is 1, when the cavitation is in the evaporation process, i is 2, R B represents a given constant term; ρ l represents the density of the liquid outside the cavitation bubble; P v represents the internal pressure of the bubble; P0 represents the ambient pressure at the initial moment of a time step; P t represents the ambient pressure at the end of a time step, C0 is the preset model coefficient; R0 represents the initial radius of the cavitation nucleus; R represents the cavitation radius; n represents the bubble number density; The expression of the modified cavitation model is as follows: Among them, R e represents the mass transfer rate of the cavitation evaporation process; R c represents the mass transfer rate of the cavitation condensation process; F vap Indicates the evaporation process coefficient; F cond represents the condensation process coefficient; α nuc represents the volume fraction of nucleation points; α represents the volume fraction of bubbles per unit volume; R B represents a given constant term; || represents the absolute value function; ρ v Indicates the gas density.

2. The cavitation model correction method considering transient effects of flow field according to claim 1, characterized in that: The expression of the modified cavitation model is as follows: The original cavitation model includes a mass transfer model based on the Rayleigh-Plesset equation that ignores gravity, surface tension, and viscous forces.

3. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 2 are implemented.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 2 are implemented.

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