Multi-scale coupling cavitation flow state prediction method for hydraulic mechanical product

Abstract

The invention discloses a multi-scale coupling cavitation flow state prediction method for a hydraulic mechanical product. Comprising the following steps; the method comprises the following steps: firstly, establishing a cavitation area grid model of the hydraulic mechanical product, and determining boundary conditions, a turbulence model and gas nucleus size distribution of the hydraulic mechanical product; then, a multi-scale coupling cavitation flow dynamic model is established, and the multi-scale coupling cavitation flow dynamic model comprises a multi-scale coupling cavitation flow control equation set, a Lagrange bubble model and an inter-scale conversion model; and finally, solving and calculating a multi-scale coupling cavitation flow value based on the cavitation area grid model, the turbulence model, the gas nucleus size distribution and the multi-scale coupling cavitation flow dynamic model to obtain macroscopic flow field velocity distribution, pressure distribution and phase distribution and micro-scale bubble position distribution and size distribution of the hydraulic mechanical product. According to the invention, the independent motion of the bubbles can be described on the micro scale, and the cavitation dynamic behavior on the macro scale is captured.

Description

Technical Field

[0001] The present invention relates to a method for predicting the cavitation flow state of a hydraulic machinery product in the field of cavitation, and specifically relates to a multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product. Background Art

[0002] Cavitation is a hydrodynamic phenomenon commonly existing in hydraulic machinery such as pumps, propellers and turbines. It usually occurs in the low-pressure area on the suction side of the blade or in the eddy current generated by the rotation of the device. In a propeller, tip vortex cavitation usually starts first, and causes an increase in noise during the operation of the propeller. In contrast, sheet cavitation will change the pressure distribution on the blade, thus affecting the efficiency of the propeller. When blade cavitation starts to shed periodically, resulting in cloud cavitation, it will generate cyclic fatigue loads, leading to serious damage to the blade. The transition from sheet cavitation to cloud cavitation involves a complex transformation of the cavity structure and potential mechanism. In this case, accurately predicting the cavitation flow field characteristics during the transition from sheet cavitation to cloud cavitation is an issue that cannot be ignored.

[0003] Experimental methods have greatly improved the understanding of sheet-cloud cavitation and its formation mechanism. However, due to the limitations of measurement means and experimental equipment, there are still difficulties in the refined measurement of the cavitation flow field cavity structure. The progress of CPU technology has made computational fluid dynamics (CFD) an effective method for studying the sheet-cloud cavitation structure and its formation mechanism. Currently, the most commonly used state prediction method is Euler cavitation simulation. This technology uses a homogeneous mixture model, in which the two-phase flow is regarded as a single phase with variable density and viscosity. A cavitation model combined with the mass transfer rate is used to simulate the phase change process. However, with the improvement of the accuracy requirements for cavitation flow simulation, the limitations of this model become more and more obvious. Precise prediction of sharp cavity interfaces and small-scale cavity structures requires high grid resolution. At the conventional grid resolution, the internal structure of the cloud cavity can hardly be distinguished in the calculation results. This method assumes that the gas nuclei in the flow field are abundant and evenly distributed, resulting in an overestimation of the internal structure of the cloud cavity. Therefore, it is necessary to improve the simulation for multi-scale bubble structures and establish a multi-scale state prediction method to accurately predict the transition process from sheet cavitation to cloud cavitation. Summary of the Invention

[0004] In order to solve the problems and requirements existing in the background art, the present invention provides a multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product. This method can accurately estimate the unsteady flow characteristics during the transition process of sheet-cloud cavitation, and obtain the macroscopic flow field velocity distribution, pressure distribution, phase distribution, and micro-scale bubble position distribution and size distribution. Thus, it provides a theoretical basis for unsteady cavitation flow and is used to solve the cavitation form prediction problem in water quality with different gas contents.

[0005] The technical solution adopted by the present invention is:

[0006] 1. A method for predicting the multi-scale coupled cavitation flow state of a hydraulic machinery product

[0007] Step 1: Establish a cavitation region grid model of the hydraulic machinery product and determine the boundary conditions, turbulence model and gas nucleus size distribution of the hydraulic machinery product;

[0008] Step 2: Establish a multi-scale coupled cavitation flow dynamics model, which includes the control equations for multi-scale coupled cavitation flow, the Lagrangian bubble model and the inter-scale conversion model;

[0009] Step 3: Based on the cavitation region grid model, turbulence model, gas nucleus size distribution and multi-scale coupled cavitation flow dynamics model, perform numerical solution calculations for multi-scale coupled cavitation flow to obtain the macroscopic flow field velocity distribution, pressure distribution and phase distribution of the hydraulic machinery product, as well as the micro-scale bubble position distribution and size distribution.

[0010] In the said Step 1, the boundary conditions specifically include:

[0011] The velocity boundary condition is adopted at the fluid inlet, the pressure boundary condition is adopted at the fluid outlet, and the no-slip boundary condition is adopted at the wall surface.

[0012] In the said Step 1, the gas nucleus size distribution is the initial gas nucleus size distribution, which is either the depletion condition or the enrichment condition, and both satisfy the normal distribution.

[0013] The gas nucleus diameter interval of the depletion condition is 1 - 10 microns; the gas nucleus diameter distribution interval of the enrichment condition is 20 - 180 microns.

[0014] In the said Step 2, the control equations for multi-scale coupled cavitation flow include the continuity equation, the momentum equation and the liquid phase volume fraction transport equation:

[0015]

[0016] Among them, ρ m is the density of the vapor-liquid mixed phase; u i is the first component of the velocity in the flow field; x i is the first component of the spatial coordinate; t is the time; u j is the second component of the velocity in the flow field; x j is the second component of the spatial coordinate; p is the pressure; μ m is the dynamic viscosity of the vapor-liquid mixed phase; α l is the liquid phase volume fraction; ρ l is the density of the liquid phase; neg() is a numerical judgment function, which returns 1 if the number in the parentheses is less than 0, otherwise it returns 0; F s and F b are the surface tension and the gas nucleus source term respectively; is the cavitation source term.

[0017] In the second step, the Lagrangian bubble model consists of a bubble motion equation and a bubble dynamic equation; the bubble motion equation satisfies the following formula:

[0018]

[0019] F g = m b g,

[0020] where F lift is the lift force, F drag is the drag force, F a is the added mass force, F vm is the volume change force, F p is the pressure gradient change force, F buoy is the buoyancy force, F g is the gravity force; R is the gas nucleus radius, m b is the gas nucleus mass, u b is the gas nucleus velocity, p c is the Eulerian flow field pressure; C D 、C L are the drag coefficient and the lift coefficient respectively; ρ l is the density of the liquid phase; u c is the velocity of the flow field around the gas nucleus, is the curl operation for calculation, ρ b is the gas nucleus density; d b is the gas nucleus diameter; || is the absolute value, is the gas nucleus wall velocity; is the pressure gradient, g is the gravitational acceleration;

[0021] The bubble dynamic equation satisfies the following formula:

[0022]

[0023] where R is the gas nucleus radius, is the gas nucleus wall acceleration, σ is the surface tension coefficient, v c is the kinematic viscosity of the liquid phase, p b is the internal pressure of the bubble, p v is the saturated vapor pressure of the bubble, R0 is the initial radius of the gas nucleus; γ is the specific heat ratio.

[0024] In the second step, the scale conversion model consists of a macroscale to microscale conversion model and a microscale to macroscale conversion model.

[0025] In the third step, in the numerical solution process of multi-scale coupled cavitation flow, the convection term adopts a second-order upwind scheme, and the transient term adopts a bounded second-order implicit scheme.

[0026] II. A computer device

[0027] The device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, the steps of the method for predicting the multi-scale coupled cavitation flow state of a hydraulic machinery product are implemented.

[0028] III. A computer-readable storage medium

[0029] A computer program is stored on the medium. When the computer program is executed by a processor, the steps of the method for predicting the multi-scale coupled cavitation flow state of a hydraulic machinery product are implemented.

[0030] The beneficial effects of the present invention are as follows:

[0031] 1. In the present invention, the cavities unresolved in the macroscopic scale are transferred to the Lagrangian microscopic scale; once they expand to be resolved, they return to the macroscopic scale, and the influence of gas nuclei on cloud cavitation is considered.

[0032] 2. Using the predicted results, the present invention observes that the change in the gas nucleus distribution significantly affects the morphology and evolution of cloud cavitation, indicating that the macroscopic cavitation flow has a significant impact on the behavior of Lagrangian bubbles.

[0033] 3. The predicted results of the present invention accurately reproduce the bubble size distribution observed in experiments, which is characterized by two different power-law scalings: the scaling for larger bubbles is -10 / 3, and the scaling for smaller bubbles is -4 / 3. These scaling behaviors remain consistent under different cavitation numbers, thus verifying the robustness of the method in predicting bubble dynamics and cavitation characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flowchart of the method of the present invention.

[0035] Figure 2 is a schematic diagram of the computational domain model of the three-dimensional NACA0015 airfoil flow field in an embodiment of the present invention.

[0036] Figure 3 is a schematic diagram of the grid division of the computational domain of the three-dimensional NACA0015 airfoil flow field in an embodiment of the present invention.

[0037] Figure 4 is a schematic diagram of the gas nucleus release region in an embodiment of the present invention.

[0038] Figure 5 is a comparison between the numerical simulation result cavitation cloud diagram and the experimental result under cloud cavitation in an embodiment of the present invention.

[0039] Figure 6It is a comparison of the lift and drag coefficients between the numerical simulation results and the experimental results under cloud cavitation in the embodiments of the present invention. Specific Embodiments

[0040] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] Embodiment In this embodiment, a three-dimensional NACA0015 hydrofoil publicly disclosed abroad is taken as the research object. The chord length c of the NACA0015 airfoil is 150 mm, the span b is 300 mm, and the maximum thickness of the airfoil is 15% of the chord length. As Figure 1 shown, the specific implementation steps of the method proposed by the present invention are as follows:

[0042] Step 1: Establish a cavitation region grid model of the hydrofoil and determine the boundary conditions, turbulence model and gas nucleus size distribution of the hydrofoil;

[0043] Taking the three-dimensional NACA0015 hydrofoil as the research object, determining the airfoil structure parameters, using software to draw the flow field calculation domain, the length of the calculation domain is 13c, and the width and height are 4c, as Figure 2 shown. Import the calculation domain model into the grid generation software, define the left and right sides of the calculation domain as the inlet and outlet respectively, the upper, lower, front and rear surfaces as the wall, and the airfoil is also the wall; and set an encryption area around the hydrofoil to meet the solution requirements of the equations, so as to capture richer cavitation flow details, as Figure 3 shown.

[0044] The boundary conditions specifically include:

[0045] The velocity boundary condition is adopted at the fluid inlet, the pressure boundary condition is adopted at the fluid outlet, and the no-slip boundary condition is adopted at the wall.

[0046] The WALE large eddy simulation calculation method is adopted for the turbulence model. The sub-grid stress of this turbulence model is:

[0047]

[0048] Among them, τ ij is the sub-grid stress, k SGS is the turbulent kinetic energy, δ ij is the Kronecker function, is the first velocity component after spatial filtering, is the second velocity component after spatial filtering, ρ is the fluid density, is the deviatoric part of the strain rate tensor, is the square of the velocity gradient tensor between the first velocity component and the second velocity component, is the square of the velocity gradient tensor between the second velocity component and the first velocity component; is the strain rate tensor, v SGS is the sub-grid eddy viscosity coefficient; k is the von Kármán constant, d is the wall distance, L s is the sub-grid mixing length, V is the volume of the computational grid cell, C w is the WALE constant, and its value is 0.325.

[0049] The gas nucleus size distribution is the initial gas nucleus size distribution, and it is either the depletion condition or the enrichment condition, both of which satisfy the normal distribution; among them, the gas nucleus diameter range under the depletion condition is 1-10 microns; the gas nucleus diameter distribution range under the enrichment condition is 20-180 microns. Under the depletion condition, the gas nucleus injection density is 1 per milliliter, and the injection density under the enrichment condition is 300 per milliliter, as Figure 4 shown. In this embodiment, the initial gas nucleus size distribution is set at a certain distance in front of the target position.

[0050] Step 2: Establish a multi-scale coupled cavitation flow dynamics model, which includes the control equations for multi-scale coupled cavitation flow, the Lagrangian bubble model, and the inter-scale conversion model;

[0051] The control equations for multi-scale coupled cavitation flow include the continuity equation, the momentum equation, and the liquid-phase volume fraction transport equation:

[0052]

[0053] Among them, ρ m is the density of the vapor-liquid mixture; u i is the first component of the velocity in the flow field; x i is the first component of the spatial coordinate; t is the time; u j is the second component of the velocity in the flow field; x j is the second component of the spatial coordinate, that is, the three direction components of the right-handed coordinate system in the cavitation region grid model corresponding to the subscripts i, j, k; p is the pressure; μ m is the dynamic viscosity of the vapor-liquid mixture; α l is the liquid-phase volume fraction; ρ l is the density of the liquid phase; neg() is a numerical judgment function that returns 1 if the number in the parentheses is less than 0, otherwise it returns 0; F s 、F b are the surface tension and the gas nucleus source term respectively, and the reaction is the effect of the gas nucleus on the flow field. is the cavitation source term, which reflects the mass transfer process between the vapor and liquid phases.

[0054] The Lagrangian bubble model consists of the bubble motion equation and the bubble dynamic equation; the bubble motion equation aims to calculate the position change of the gas nucleus in the flow field movement and satisfies the following formula:

[0055]

[0056] F g = m b g,

[0057] where F lift is the lift force, F drag is the drag force, F a is the added mass force, F vm is the volume change force, F p is the pressure gradient change force, F buoy is the buoyancy force, F g is the gravitational force; R is the radius of the gas nucleus, m b is the mass of the gas nucleus, u b is the velocity of the gas nucleus, p c is the pressure of the Euler flow field; C D , C L are the drag coefficient and the lift coefficient respectively; ρ l is the density of the liquid phase; u c is the velocity of the flow field around the gas nucleus, is the curl operation; ρ b is the density of the gas nucleus; d b is the diameter of the gas nucleus; || is the absolute value, is the wall velocity of the gas nucleus; is the pressure gradient, g is the acceleration due to gravity;

[0058] The drag coefficient C D and the lift coefficient C L can be expressed by the following empirical formula:

[0059]

[0060] where Re b is the Reynolds number of the gas nucleus, Re w is the vorticity Reynolds number of the gas nucleus, u is the fluid velocity, μ is the dynamic viscosity.

[0061] The bubble dynamic equation aims to describe the growth and collapse behavior of cavitation gas nuclei in the pressure field. Usually, the classical Rayleigh - Plesset (R - P) equation is used to solve the radius change of the gas nucleus. The R - P equation satisfies the following formula:

[0062]

[0063] where R is the radius of the gas nucleus, is the wall acceleration of the gas nucleus, σ is the surface tension coefficient, v c is the kinematic viscosity of the liquid phase, p b is the pressure inside the bubble, pv Here, \(p_{v}\) is the saturated vapor pressure of the bubble, \(R_{0}\) is the initial radius of the gas nucleus; \(\gamma\) is the specific heat ratio. When the gas nucleus expands, it is regarded as an isothermal process with \(\gamma = 1\). When the gas nucleus collapses, it is regarded as an adiabatic process with \(\gamma = 1.4\).

[0064] The scale conversion model consists of a macro-scale to micro-scale conversion model and a micro-scale to macro-scale conversion model. Among them, the macro-scale to micro-scale conversion model aims to solve the grid resolution limitation inside the captured cavitation structure, and uses the Lagrangian bubble model to track the conversion of small-scale cavitation bubbles in the macro-framework to the micro-scale. The micro-scale to macro-scale conversion specifically means that the gas nucleus in the micro-framework grows and expands in the low-pressure area until it reaches a threshold and then is converted to the macro-scale, specifically tracked using the governing equations.

[0065] Step 3: Based on the cavitation region grid model, turbulence model, gas nucleus size distribution, and multi-scale coupled cavitation flow dynamics model, perform numerical solution calculations of multi-scale coupled cavitation flow to obtain the macroscopic flow field velocity distribution, pressure distribution, and phase distribution of the hydrofoil, as well as the micro-scale bubble position distribution and size distribution. Adjust the design parameters of the hydrofoil according to the obtained macroscopic flow field velocity distribution, pressure distribution, phase distribution, micro-scale bubble position distribution, size distribution, and actual requirements, so as to suppress cavitation. The present invention can describe the independent movement of bubbles at the micro-scale, while capturing the cavitation dynamics behavior at the macro-scale, and more realistically reproduce the multi-scale flow characteristics during cavitation, from the birth, development to shedding of bubbles, providing a physically realistic solution for simulating complex unsteady cavitation flow structures.

[0066] Among them, in the process of numerical solution calculation of multi-scale coupled cavitation flow, the convection term adopts a second-order upwind scheme, and the transient term adopts a bounded second-order implicit scheme. A fixed time step is used to keep the CFL number less than 1. The pressure-implicit with splitting of operators (PISO) algorithm is used to solve the velocity and pressure coupling equations to obtain the macroscopic flow field velocity distribution, pressure distribution, and phase distribution. The bubble motion equation is solved using the first-order implicit Euler scheme, and the bubble dynamics equation is solved using the fourth-order Runge-Kutta method to obtain the micro-scale bubble position distribution and size distribution. The post-processing of the prediction results is shown as Figure 5 as Figure 6 shown, which are respectively the comparison of the periodic evolution of the cavitation bubble morphology within a cycle and the experimental results in the cloud cavitation of the embodiment of the present invention, as well as the corresponding comparison results of the lift and drag coefficients. Figure 5 (a) of Figure 5 is the experimental observation result under the depletion condition, Figure 5 and (b) of Figure 5 is the multi-scale simulation result under the depletion condition, Figure 5(e) is the simulation result of the Euler model. In the flow under depletion conditions, as the cavitation number decreases, the cavity expands outward along the spanwise and chordwise directions. The multi-scale model accurately reproduces the shape of these cavities. Under the condition of rich nuclei, both the multi-scale model and the Euler model predict similar cavity shapes, and these cavity shapes mainly increase as the cavitation number decreases. Figure 6 (a) of which is the comparison of the time-averaged lift coefficient, Figure 6 (b) of which is the comparison of the time-averaged drag coefficient. As Figure 6 shown, the time-averaged lift coefficient obtained by the multi-scale model under depletion and rich conditions is in good agreement with the experimental results. Compared with the Euler model, the multi-scale model shows excellent performance under depletion conditions at all cavitation numbers. However, under rich conditions, the simulation results of the multi-scale model and the Euler model are almost the same.

[0067] Finally, it should be noted that the above embodiments and descriptions are only used to illustrate the technical solutions of the present invention rather than to limit them. Those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced. Without departing from the spirit and scope of the disclosure of the technical solutions of the present invention, they should all be covered by the protection scope of the claims of the present invention.

Claims

1. A multi-scale coupled cavitation flow state prediction method for hydraulic machinery products, characterized in that: The following steps are involved: Step 1: Establish the cavitation area grid model of hydraulic machinery products and determine the boundary conditions, turbulence model and gas core size distribution of hydraulic machinery products; Step 2: Establish a multi-scale coupled cavitation flow dynamics model, which includes the control equations of multi-scale coupled cavitation flow, the Lagrangian bubble model and the inter-scale conversion model; Step 3: Based on the cavitation area grid model, turbulence model, gas core size distribution and multi-scale coupled cavitation flow dynamics model, the multi-scale coupled cavitation flow numerical solution calculation is performed to obtain the macroscopic flow field velocity distribution, pressure distribution and phase distribution of the hydraulic machinery product as well as the micro-scale bubble position distribution and size distribution.

2. The multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product according to claim 1 is characterized in that: In the step 1, the boundary conditions specifically include: Velocity boundary conditions are used at the fluid inlet, pressure boundary conditions are used at the fluid outlet, and no-slip boundary conditions are used on the wall.

3. The multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product according to claim 1 is characterized in that: In the step 1, the gas core size distribution is the initial gas core size distribution, which is a depletion condition or an abundance condition, and both satisfy the normal distribution.

4. The multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product according to claim 3 is characterized in that: The gas core diameter range under the depletion condition is 1-10 microns; the gas core diameter distribution range under the abundant condition is 20-180 microns.

5. The multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product according to claim 1 is characterized in that: In step 2, the control equations of the multi-scale coupled cavitation flow include the continuity equation, the momentum equation and the liquid phase volume fraction transport equation: Among them, ρ m is the density of the vapor-liquid mixed phase; u i is the first component of velocity in the flow field; x i is the first component of the spatial coordinate; t is time; u j is the second component of velocity in the flow field; x j is the second component of the spatial coordinate; p is the pressure; μ m is the dynamic viscosity of the vapor-liquid mixture; α l is the liquid volume fraction; ρ l is the density of the liquid phase; neg() is a numerical judgment function, which returns 1 if the number in the brackets is less than 0, otherwise it returns 0; F s 、F b are the surface tension and gas core interaction source terms respectively; is the cavitation source term.

6. The multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product according to claim 1 is characterized in that: In step 2, the Lagrangian bubble model consists of a bubble motion equation and a bubble dynamic equation; the bubble motion equation satisfies the following formula: F g =m b g, Among them, F lift is the lift, F drag is the resistance, F a is the additional mass force, F vm is the volume change force, F p is the pressure gradient change force, F buoy is the buoyancy, F g is gravity; R is the radius of the gas core, m b is the mass of the gas core, u b is the velocity of the gas core, p c is the Euler flow field pressure; C D , C L are the drag coefficient and lift coefficient respectively; ρ l is the density of the liquid phase; u c is the velocity of the flow field around the gas core, To calculate the curl operation, ρ b is the density of the gas core; d b is the diameter of the gas core; | | is the absolute value, is the velocity of the gas core wall; is the pressure gradient, g is the gravitational acceleration; The bubble dynamic equation satisfies the following formula: Where R is the radius of the gas core, is the acceleration of the gas core wall, σ is the surface tension coefficient, ν c is the liquid phase kinematic viscosity, p b The pressure inside the bubble, p v is the saturated vapor pressure of the bubble, R0 is the initial radius of the gas core; γ is the specific heat ratio.

7. The multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product according to claim 1 is characterized in that: In the step 2, the scale conversion model consists of a macro-scale to micro-scale conversion model and a micro-scale to macro-scale conversion model.

8. The multi-scale coupled cavitation flow state prediction method for a hydraulic machinery product according to claim 1 is characterized in that: In the step three, in the numerical solution and calculation process of the multi-scale coupled cavitation flow, the convection term adopts the second-order upwind format, and the transient term adopts the bounded second-order implicit format.

9. 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 8 are implemented.

10. 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 8 are implemented.

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