CN115293004A - Cavitation erosion prediction method based on multi-scale cavitation model - Google Patents
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Abstract
The invention discloses a cavitation erosion prediction method based on a multi-scale cavitation model, which comprises the following steps of; carrying out grid division on a preset calculation domain, and determining boundary conditions, physical parameters of gas-liquid two phases and mass transfer rates of liquid and gas phases caused by cavitation; capturing an interface between gas phase and liquid phase caused by phase change by adopting an interface capturing method, searching the position of the interface, reconstructing the interface or optimizing the interface precision by adopting an interface compression method and the like; and searching the broken position of the interface, identifying the broken small-scale bubbles, converting the small-scale bubbles into dispersion bubbles, and tracking and solving by adopting a satellite method. And coupling the cavitation flow with the continuous phase to realize multi-scale simulation of the cavitation flow. Has the advantages that: the method is implemented on the basis of an interface capture method based on a finite volume method, and adopts a dynamic grid self-adaptive method to ensure that the interface precision meets the set requirement, so that the calculation of the cavitation erosion rate of the surface of the prediction model is more intuitive and accurate.
Description
Technical Field
The invention relates to the technical field of fluid machinery and cavitation flow simulation, in particular to a cavitation erosion prediction method based on a multi-scale cavitation model.
Background
Cavitation is a common phenomenon inside hydraulic machinery, and its unsteady characteristics are the main causes of pressure pulsation, vibration, noise and cavitation in water pumps, water turbines, underwater propellers and complex piping systems. On the other hand, the development of the supercavitation technology provides a new means for increasing the speed of the underwater weapon or the navigation body, and the navigation body can avoid the viscous resistance of water under the condition of gas wrapping by utilizing the supercavitation technology, so that the underwater ultrahigh-speed navigation is realized. The application of the supercavitation technology also poses great challenges to the control and motion stability of the navigation body. Whether cavitation in hydraulic machinery or application of a supercavitation technology, a complex flow field structure with multiple time and space scales caused by cavitation breaking and cavitation cloud collapse is a main reason for the adverse effects, and is also a hotspot and difficulty of research. In the research aiming at engineering problems, a macroscopic flow law can be obtained by an averaging method, but cavitation shows special unsteady and transient characteristics, and the averaging processing in calculation causes the reflection distortion of objective phenomena and laws. With the research on the cavitation problem, it is necessary to discuss the migration and collapse rule of micro-scale cavitation bubbles.
Cavitation is that the liquid can form bubbles locally due to impact of jet shock waves generated by cavitation collapse, and pressure waves are generated in the processes of continuous condensation, development and collapse to form local high temperature and high pressure, so that the surface of the material is degraded and damaged. Due to the complexity of the cavitation flow process, a large amount of manpower and material resources are consumed in experiments, data measurement is difficult, the cavitation flow process is usually accompanied by very complex interphase mass transfer, a multi-scale gas-liquid two-phase structure and a turbulent flow structure, instability of a cavity form and turbulence vibration caused by the instability, and the like, and the phenomena undoubtedly cause great challenges to cavitation numerical value research and cavitation erosion prediction. The cavitation flow process often comprises a cavity interface with a larger scale and dispersion bubbles generated by crushing, and the traditional numerical calculation method does not consider the micro-cavitation bubble migration and collapse processes, so that the prediction of a cavitation erosion area and the risk thereof is deviated, so that perfect simulation needs to be performed on a multi-scale cavitation bubble structure, a multi-scale numerical calculation method is established, and the prediction of cavitation erosion is carried out on the basis of the multi-scale numerical calculation method.
An effective solution to the problems in the related art has not been proposed yet.
Disclosure of Invention
Aiming at the problems in the related art, the invention provides a cavitation erosion prediction method based on a multi-scale cavitation model, so as to overcome the technical problems in the prior related art.
Therefore, the invention adopts the following specific technical scheme:
a cavitation erosion prediction method based on a multi-scale cavitation model comprises the following steps;
s1, carrying out grid division on a preset calculation domain, and determining boundary conditions, physical parameters of gas-liquid two phases and mass transfer rates of liquid and gas phases caused by cavitation;
s2, capturing an interface between gas phase and liquid phase caused by phase change by adopting an interface capturing method, searching the position of the interface, reconstructing the interface or optimizing the interface precision by adopting an interface compression method and the like;
s3, searching the position of interface breakage, identifying broken small-scale bubbles, converting the broken small-scale bubbles into dispersion bubbles, and tracking and solving by adopting a satellite method. Coupling the cavitation flow with a continuous phase to realize multi-scale simulation of the cavitation flow;
and S4, establishing a cavitation erosion prediction method based on the multi-scale cavitation model.
Preferably, the interface in S2 is a continuous boundary of a large-scale cavity, the cavity boundary is captured and reconstructed based on a spatial grid, the interface accuracy is determined according to the spatial grid scale, a high-accuracy interface capture method such as a dynamic grid adaptive method can be appropriately adopted, and the small-scale bubbles in S3 are small bubbles that cannot be identified by a computational grid formed by crushing the large-scale cavity.
Preferably, after the step S1 is implemented, a continuous cavitation interface capturing algorithm, a grid dynamic splitting method, a dispersion bubble satellite algorithm, a dispersion bubble growth collapse and merging crushing model, and an interface and dispersion bubble conversion algorithm, in which the volume fraction of the dispersion bubbles is occupied, are integrated in the established multi-scale cavitation model.
Preferably, the continuous cavity interface capturing algorithm with the volume fraction occupied by the dispersed bubbles in the set comprises the following specific steps:
(a1) The distribution of the gas phase volume fraction alpha in the cavitation flow is obtained by adopting a formula I:
the formula I is as follows: (ii) a Wherein R represents the mass transfer rate between gas phase and liquid phase caused by cavitation, R b A source term caused by fusion of dispersed bubbles and continuous cavitation bubbles, wherein u represents the speed;
the left side of the first formula can also include an interface compression term to prevent interface divergence:
wherein u is α Interface compression rate:
the direction is always vertical to the interface; c α Is a compression factor; the interface compression term only works at the interface, i.e. 0 < alpha < 1.
(a2) And acquiring the volume fraction of the dispersed bubbles according to a formula II:
the formula II is as follows:
wherein, for the set minimum volume fraction value, the situation that epsilon is less than 1 is prevented; v b ,V cell Respectively represent bubblesVolume and cell volume where the bubble is located;
(a3) Solving a continuity equation and a momentum equation of the gas-liquid two-phase fluid in consideration of the volume fraction of the dispersed bubbles according to a third formula and a fourth formula:
the formula III is as follows:
the formula four is as follows:
wherein: u. of c Representing continuous phase velocity, P representing pressure, S representing viscous stress tensor, g representing gravitational acceleration, F b ,F s Respectively, the force and surface tension of the dispersed bubbles on the continuous phase.
(a4) And acquiring the surface tension according to a formula V: f s
The formula five is as follows:
where γ is a surface tension coefficient determined from physical parameters of gas and liquid, and κ is a curvature of an interface, and can be expressed as:
(a5) And acquiring the acting force of the dispersed bubbles on the continuous phase according to a formula six: f b
The formula six:
wherein beta is a drag coefficient, F other Representing other interphase forces than drag.
Preferably, the grid dynamic splitting method includes the specific steps of: and judging whether the gas volume fraction of the cell is between 0 and 1, if so, determining the interface position, subdividing the mesh by two middle sections (three-dimensional) or middle lines (two-dimensional), if so, stopping the splitting of the mesh, and if not, continuously subdividing the sub-mesh.
Preferably, the dispersion bubble satellite algorithm specifically comprises the following steps: and obtaining the speed of the dispersed bubbles according to a formula seven:
the formula is seven:
in the formula: m is b ，u b Respectively representing the mass and velocity of the dispersed bubbles; f C Represents the force between the bubbles, F' b Representing the reaction force of the continuous phase against the bubble, F b The sizes are the same, and the directions are opposite;
preferably, the bubble dispersion continuous transition algorithm can be mainly divided into three parts, nine large holes are analyzed by the model through an interface capture method, the sub-grid-scale bubbles are simulated through a Lagrange's formula, and the transition from dispersed bubbles growing to fill cells to a continuous gas phase is firstly carried out. Secondly, the fusion between the dispersed bubbles and the continuous gas phase, and finally, the continuous gas phase becomes unresolvable and is converted into the dispersed bubbles, since the limit of the volume fraction of the randomly-stacked dispersed phase is about 0.6, =0.6 is selected as the standard and the threshold of the latter two conversions, once the dispersed bubbles are converted into the continuous gas phase, the dispersed bubbles are deleted, and the mass of the dispersed bubbles is added into the resolved cavity.
Preferably, the complete description of the multi-scale different cavitation forms is realized by accurately simulating a larger-scale cavity interface and small-scale dispersed bubbles. Therefore, the cavitation erosion area and the cavitation erosion probability of each area can be effectively predicted, and the specific steps are as follows:
the cavitation erosion is caused by potential energy contained in the cavitation bubbles released when the cavitation bubbles close to the surface of the material collapse;
(a6) Acquiring a pressure wave when the cavity structure collapses according to the formula eight:
the formula eight:
wherein P represents a reference pressure field driving collapse of cavitation bubbles, P v Denotes the saturation pressure, V b Indicating the void volume.
(a7) Calculating the cavitation collapse potential pressure density according to the formula nine:
the formula is nine:
wherein (alpha + alpha) v ) Indicating the volume fraction of vacuoles.
(a8) Calculating the cavitation erosion rate of the model according to the formula ten:
formula ten:
(a9) Calculating the cavitation rate prediction accumulated over time for the model according to the formula eleven:
formula eleven:
on the other hand, to address the risk of cavitation erosion of the surface, a cavitation risk indicator according to the formula twelve is used herein:
equation twelve:
wherein (E) t ) et As a total cavitation rate E t The normalized parameter has a cavitation rate gradually reaching a peak value as the parameter n increases.
The invention has the beneficial effects that: the implementation of the invention is based on an interface capture method based on a finite volume method, and adopts a dynamic grid self-adaptive method to ensure that the interface precision reaches the set requirement, thereby ensuring that the calculation of the cavitation erosion rate of the surface of the prediction model is more intuitive and accurate:
the method can realize direct solution of the large-scale cavitation bubble boundary so as to obtain morphological characteristics of deformation, instability, splitting and the like of the large-scale cavitation bubble, and can predict cavitation erosion distribution of the model surface through numerical calculation.
The small bubbles can be tracked and solved to describe the small bubbles which are difficult to describe by an interface capture method, so that the individual motion behaviors of the small bubbles are simulated and coupled with the continuous phase, and the cavitation erosion damage degree of each area of the model interface is more accurately and comprehensively predicted.
The method can avoid capturing all small bubble interfaces so as to consume a large amount of computing resources, can describe the motion behavior of the small bubbles more perfectly, saves the experimental computing cost and time, and provides help for the cavitation erosion optimization design of the model.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a schematic flow chart of a cavitation erosion prediction method based on a multi-scale cavitation model according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of cavitation bubbles in a cavitation erosion prediction method based on a multi-scale cavitation model according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a bubble dispersion continuous transition algorithm in a cavitation erosion prediction method based on a multi-scale cavitation model according to an embodiment of the present invention.
Detailed Description
For further explanation of the various embodiments, the drawings which form a part of the disclosure and which are incorporated in and constitute a part of this specification, illustrate embodiments and, together with the description, serve to explain the principles of operation of the embodiments, and to enable others of ordinary skill in the art to understand the various embodiments and advantages of the invention, and, by reference to these figures, reference is made to the accompanying drawings, which are not to scale and wherein like reference numerals generally refer to like elements.
According to an embodiment of the invention, a cavitation erosion prediction method based on a multi-scale cavitation model is provided.
As shown in fig. 1-3, a cavitation erosion prediction method based on multi-scale cavitation model according to an embodiment of the present invention includes the following steps;
s1, carrying out grid division on a preset calculation domain, and determining boundary conditions, physical parameters of gas-liquid two phases and mass transfer rates of liquid and gas phases caused by cavitation;
s2, capturing an interface between gas and liquid phases caused by phase change by adopting an interface capturing method, searching the position of the interface, and reconstructing the interface or optimizing the precision of the interface by adopting an interface compression method and the like;
s3, searching the position of interface breakage, identifying broken small-scale bubbles, converting the broken small-scale bubbles into dispersion bubbles, and tracking and solving by adopting a satellite method. Coupling the cavitation flow with a continuous phase to realize multi-scale simulation of the cavitation flow;
and S4, establishing a cavitation erosion prediction method based on the multi-scale cavitation model.
In addition, in an embodiment, the interface in S2 is a continuous boundary of a larger-scale void, the void boundary is captured and reconstructed based on a spatial grid, the interface precision is determined according to the spatial grid scale, a high-precision interface capture method such as a dynamic grid adaptive method may be appropriately adopted, and the small-scale bubble in S3 is a small bubble that cannot be identified by a computational grid formed by crushing the large-scale void.
After the S1 is implemented, a continuous cavitation interface capturing algorithm, a grid dynamic splitting method, a dispersion bubble satellite algorithm, a dispersion bubble growth collapse and merging crushing model and an interface and dispersion bubble conversion algorithm which are integrated with the volume fraction occupied by the dispersion bubbles are built in the established multi-scale cavitation model.
In addition, in one embodiment, the continuous cavity interface capturing algorithm for collecting the volume fraction occupied by the dispersed bubbles specifically includes the following steps:
(a1) The distribution of the gas phase volume fraction alpha in the cavitation flow is obtained by adopting a formula I:
the formula I is as follows:(ii) a Wherein R represents the mass transfer rate between gas and liquid phases caused by cavitation, R b A source term caused by fusion of dispersed bubbles and continuous cavitation bubbles, wherein u represents the speed;
the left side of the first formula can also include an interface compression term to prevent interface divergence:
wherein u is α Interface compression rate:
the direction is always vertical to the interface; c α Is a compression factor; the interface compression term only works at the interface, i.e. 0 < alpha < 1.
(a2) And acquiring the volume fraction of the dispersed bubbles according to a formula II:
the second formula is as follows:
wherein, for the set minimum volume fraction value, the situation that epsilon is less than 1 is prevented; v b ,V cell Respectively representing the volume of the bubbles and the volume of the cells where the bubbles are located;
(a3) Solving a continuity equation and a momentum equation of the gas-liquid two-phase fluid in consideration of the volume fraction of the dispersed bubbles according to a third formula and a fourth formula:
the formula III is as follows:
the formula four is as follows:
wherein: u. u c Representing continuous phase velocity, P representing pressure, S representing viscous stress tensor, g representing gravitational acceleration, F b ,F s Respectively, the force and surface tension of the dispersed bubbles on the continuous phase.
(a4) And acquiring the surface tension according to a formula V: f s
The formula five is as follows:
where γ is a surface tension coefficient determined from physical parameters of gas and liquid, and κ is a curvature of an interface, and can be expressed as:
(a5) And acquiring the acting force of the dispersed bubbles on the continuous phase according to a formula six: f b
Formula six:
wherein beta is a drag coefficient, F other Representing other interphase forces than drag forces.
In addition, in one embodiment, the grid dynamic splitting method includes the specific steps of: judging whether the gas volume fraction of the cell is between 0 and 1, if so, determining the interface position, subdividing the mesh by two middle sections (three-dimensional) or middle lines (two-dimensional), if the required precision is achieved, stopping the mesh splitting, and if not, subdividing the sub-mesh continuously;
the dispersion bubble satellite algorithm specifically comprises the following steps: and obtaining the speed of the dispersed bubbles according to a formula seven: .
The formula seven:
in the formula: m is b ，u b Respectively representing the mass and velocity of the dispersed bubbles; f C Represents a force between bubbles, F' b Representing the reaction force of the continuous phase against the bubble, F b The sizes are the same, and the directions are opposite;
in addition, in one embodiment, the bubble dispersion continuous transition algorithm can be mainly divided into three parts, and the model analyzes nine large holes through an interface capture method and simulates the transition from dispersed bubbles growing to fill cells to a continuous gas phase through a Lagrange formula. Secondly, the fusion between the dispersed bubbles and the continuous gas phase, and finally, the continuous gas phase becomes unresolvable and is converted into the dispersed bubbles, since the limit of the volume fraction of the randomly-stacked dispersed phase is about 0.6, =0.6 is selected as the standard and the threshold of the latter two conversions, once the dispersed bubbles are converted into the continuous gas phase, the dispersed bubbles are deleted, and the mass of the dispersed bubbles is added into the resolved cavity.
In addition, in one embodiment, complete description of the multi-scale different cavitation forms is achieved by accurately simulating the larger-scale cavity interface and the small-scale dispersed bubbles. Therefore, the cavitation erosion area and the cavitation erosion probability of each area can be effectively predicted, and the specific steps are as follows:
cavitation erosion is caused by the intrinsic potential energy released by cavitation bubbles near the surface of the material when collapsing;
(a6) Acquiring pressure waves when the cavity structure collapses according to the formula eight:
the formula eight:
wherein P represents a reference pressure field driving collapse of cavitation bubbles, P v Denotes the saturation pressure, V b Indicating the void volume.
(a7) Calculating the cavitation collapse potential pressure density according to the formula nine:
the formula is nine:
wherein (alpha + alpha) v ) Indicating the volume fraction of vacuoles.
(a8) Calculating the cavitation erosion rate of the model according to the formula ten:
formula ten:
(a9) Calculating the cavitation rate prediction accumulated over time for the model according to the formula eleven:
formula eleven:
on the other hand, to address the risk of cavitation erosion of the surface, a cavitation risk indicator according to the formula twelve is used herein:
equation twelve:
wherein (E) t ) et As a total cavitation rate E t The normalized parameter has a cavitation rate gradually reaching a peak value as the parameter n increases.
In addition, in an embodiment, fig. 2 is a cavitation bubble structure obtained by performing simulation calculation on cavitation flow by using the multi-scale adaptive model provided by the invention, and the form and the evolution process of the large-scale cavitation bubble at the front part are calculated by an interface capture method; due to the adoption of the self-adaptive optimization of the grids, cavitation clouds generated by the crushing of large-scale cavitation bubbles can be captured by the small grids after the separation; if the small bubbles still cannot be captured by the split grids, the small bubbles are converted into dispersion bubbles, tracking solution is carried out by a satellite method, and the motion trail of the small-scale bubbles and the interaction between the small-scale bubbles and the fluid are calculated, so that the cavitation erosion area and the cavitation erosion damage degree of the surface of the model are effectively predicted.
In addition, in an embodiment, fig. 3 illustrates a bubble dispersion continuous transition algorithm proposed by the present invention, and the transition algorithm can be mainly divided into three parts, as shown in fig. 3. The model analyzes 9 large holes by an interface capture method, and simulates bubbles with a sub-grid scale by a Lagrange formula. First from the dispersed bubbles that are growing to fill the cell to a continuous gas phase. Secondly, the fusion between the dispersed bubbles and the continuous gas phase, and finally, the continuous gas phase becomes unresolvable and is converted into the dispersed bubbles. Since the limit of randomly packed dispersed phase volume fraction is about 0.6, =0.6 was chosen as the criterion and threshold for the latter two transformations. Once the dispersed bubble has been converted to a continuous gas phase, it is removed and its mass added to the resolved cavity
In summary, with the aid of the technical solutions of the present invention, through
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (9)
1. A cavitation erosion prediction method based on a multi-scale cavitation model is characterized by comprising the following steps;
s1, carrying out grid division on a preset calculation domain, and determining boundary conditions, physical parameters of gas-liquid two phases and mass transfer rates of liquid and gas phases caused by cavitation;
s2, capturing an interface between gas phase and liquid phase caused by phase change by adopting an interface capturing method, searching the position of the interface, reconstructing the interface or optimizing the interface precision by adopting an interface compression method and the like;
s3, searching the position of interface breakage, identifying broken small-scale bubbles, converting the broken small-scale bubbles into dispersion bubbles, and tracking and solving by adopting a satellite method. Coupling the cavitation flow with a continuous phase to realize multi-scale simulation of the cavitation flow;
and S4, establishing a cavitation erosion prediction method based on the multi-scale cavitation model.
2. The cavitation erosion prediction method based on the multi-scale cavitation model according to claim 1, wherein the interface in S2 is a continuous boundary of a larger-scale cavitation bubble, the cavitation bubble boundary is captured and reconstructed based on a spatial grid, the interface precision is determined according to the spatial grid scale, a high-precision interface capture method such as a dynamic grid adaptive method can be suitably adopted, and the small-scale bubble in S3 is a small bubble which cannot be identified by a computational grid formed by breaking the large-scale cavitation bubble.
3. The cavitation erosion prediction method based on the multi-scale cavitation model according to claim 2 is characterized in that after the step S1 is implemented, a continuous cavitation interface capture algorithm, a grid dynamic splitting method, a dispersion bubble satellite algorithm, a dispersion bubble growth collapse and merging and crushing model and an interface and dispersion bubble conversion algorithm, all of which are integrated with volume fractions occupied by dispersion bubbles, are built in the multi-scale cavitation model.
4. The cavitation erosion prediction method based on multi-scale cavitation model according to claim 3,
the continuous cavity interface capturing algorithm integrating the volume fraction occupied by the dispersed bubbles comprises the following specific steps:
(a1) The distribution of the gas phase volume fraction alpha in the cavitation flow is obtained by adopting a formula I:
the formula I is as follows:
wherein R represents the mass transfer rate between gas and liquid phases caused by cavitation, R b A source term caused by fusion of dispersed bubbles and continuous cavitation bubbles, wherein u represents the speed;
the left side of the first formula may also include an interface compression term to prevent interface divergence:
wherein u is α Interface compression rate:
the direction is always vertical to the interface; c α Is the compression factor; the interface compression term only works at the interface, i.e. 0 < alpha < 1.
(a2) And acquiring the volume fraction epsilon of the dispersed bubbles according to a formula II:
the formula II is as follows:
wherein epsilon min Preventing epsilon for a set minimum volume fraction valueLess than 1; v b ,V cell Respectively representing the volume of the bubbles and the volume of the cells where the bubbles are located;
(a3) Solving a continuity equation and a momentum equation of the gas-liquid two-phase fluid in consideration of the volume fraction of the dispersed bubbles according to a third formula and a fourth formula:
the formula III is as follows:
the formula IV is as follows:
wherein: u. of c Representing continuous phase velocity, P representing pressure, S representing viscous stress tensor, g representing gravitational acceleration, F b ,F s Respectively, the force and surface tension of the dispersed bubbles on the continuous phase.
(a4) According to the formula five, the surface tension F is obtained s ：
The formula five is as follows:
where γ is a surface tension coefficient determined from physical parameters of gas and liquid, and κ is a curvature of an interface, and can be expressed as:
(a5) And acquiring the acting force of the dispersed bubbles on the continuous phase according to a formula six: f b
Formula six:
wherein beta is a drag coefficient, F other Representing other interphase forces than drag forces.
5. The cavitation erosion prediction method based on the multi-scale cavitation model as claimed in claim 4 is characterized in that the grid dynamic splitting method comprises the following specific steps: and judging whether the gas volume fraction of the cell is between 0 and 1, if so, determining the interface position, subdividing the mesh by two middle sections (three-dimensional) or middle lines (two-dimensional), if so, stopping the splitting of the mesh, and if not, continuously subdividing the sub-mesh.
6. The cavitation erosion prediction method based on the multi-scale cavitation model according to claim 5, wherein the dispersion bubble satellite algorithm comprises the following specific steps: and obtaining the speed of the dispersed bubbles according to a formula seven: .
The formula seven:
in the formula: m is b ，u b Respectively representing the mass and velocity of the dispersed bubbles; f C Represents a force between bubbles, F' b Representing the reaction force of the continuum with respect to the bubble, F b The same size, opposite direction.
7. The cavitation erosion prediction method based on the multi-scale cavitation model as claimed in claim 6 is characterized in that the bubble dispersion continuous transition algorithm, the transition algorithm can be mainly divided into three parts, the model resolves nine large holes through an interface capture method, and simulates sub-grid scale bubbles through Lagrange's formula, and the transition from dispersed bubbles growing to fill cells to a continuous gas phase is firstly carried out. Secondly, the mixing between the dispersed bubbles and the continuous gas phase, and finally, the continuous gas phase becomes unresolvable and is converted into the dispersed bubbles, since the limit of the volume fraction of the dispersed phase randomly piled is about 0.6, =0.6 is selected as the standard and the threshold value of the latter two conversions, once the dispersed bubbles are converted into the continuous gas phase, the dispersed bubbles are deleted, and the mass of the dispersed bubbles is added into the resolved cavity.
8. The cavitation erosion prediction method based on the multi-scale cavitation model according to claim 7 is characterized in that complete description of different cavitation forms in multiple scales is realized by accurately simulating a larger-scale cavity interface and small-scale dispersion bubbles. Therefore, the cavitation erosion area and the cavitation erosion probability of each area can be effectively predicted, and the specific steps are as follows:
cavitation erosion is caused by the potential energy contained in the cavitation bubbles near the surface of the material which are released when the material collapses;
(a6) Acquiring pressure waves when the cavity structure collapses according to the formula eight:
the formula eight:
wherein P represents a reference pressure field driving collapse of cavitation bubbles, P v Denotes the saturation pressure, V b Indicating the void volume.
(a7) Calculating the cavitation collapse potential pressure density according to the formula nine:
the formula is nine:
wherein (alpha + alpha) v ) Indicating the volume fraction of vacuoles.
(a8) Calculating the cavitation erosion rate of the model according to the formula ten:
formula ten:
(a9) Calculating the cavitation rate prediction accumulated over time for the model according to the formula eleven:
formula eleven:
on the other hand, to address the risk of cavitation erosion of the surface, a cavitation risk indicator according to the formula twelve is used herein:
equation twelve:
wherein (E) t ) et As a total cavitation rate E t The normalized parameter has a cavitation rate gradually reaching a peak value as the parameter n increases.
9. A multi-scale cavitation model based cavitation prediction method according to claims 1-8, characterized in that the multi-scale cavitation model comprises: liquids, gases, and dispersed bubbles.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117476039A (en) * | 2023-12-25 | 2024-01-30 | 西安理工大学 | Acoustic signal-based primary cavitation early warning method for water turbine |
| CN117476039B (en) * | 2023-12-25 | 2024-03-08 | 西安理工大学 | Acoustic signal-based primary cavitation early warning method for water turbine |
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