A three-dimensional fluid interface tracking method for unstructured grid finite volume method

Abstract

The invention provides a three-dimensional fluid interface tracking method for an unstructured grid finite volume method, relates to the field of computational fluid dynamics, and solves the problems of complex iterative calculation and low efficiency when the existing method is applied to fluid interface tracking; the method comprises: for multiple control bodies in an unstructured grid, a variational method is combined with a VOF method to determine the optimal fluid interface normal direction; in the variational method, according to the Taylor formula and a target functional, the fluid volume fraction of a certain control body is used to calculate the fluid volume fraction of its adjacent control body, and a target functional is defined: the absolute value sum of the difference between the fluid volume fraction calculated by the Taylor formula of all control bodies adjacent to a certain control body and the current actual fluid volume fraction; by calculating the target functional, the optimal fluid interface normal direction is obtained, and then the three-dimensional fluid interface tracking is completed; the solution of the invention is fast and efficient, so that the numerical simulation result has good mass conservation.

Description

Technical Field

[0001] The invention relates to the field of computational fluid dynamics, is applied to a fluid interface tracking process, and specifically relates to a three-dimensional fluid interface tracking method for an unstructured grid finite volume method. Background Art

[0002] The phenomenon of gas-liquid two-phase flow is of great significance in many fields such as aerospace, water conservancy and energy industry. In the numerical simulation of two-phase flow involving a clearly defined fluid interface, accurate tracking of the fluid interface is crucial to improving the accuracy of the simulation results. When the two-phase fluids meet at the interface, the difference in their physical properties will lead to the formation of contact discontinuities, which in turn affects the dynamic behavior of the fluid. Therefore, accurately describing the movement and deformation of the fluid interface is one of the key issues in the numerical simulation of two-phase flow.

[0003] At present, the main methods used to track fluid interfaces include the level set method, the volume of fluid (VOF) method, the phase field method, the wavefront tracking method, and the arbitrary Lagrangian-Euler (ALE) method, etc. Among them, the VOF method is widely used because of its simple concept, ability to better maintain mass conservation, and easy implementation.

[0004] VOF methods can be further divided into geometric and algebraic types according to the different ways they deal with convective transport. Geometric VOF methods can provide clear interface representation by reconstructing the free interface inside the grid cells, thereby reducing the risk of interface blur. This type of method can be further divided into two subtypes: simple linear interface calculation (SLIC) and piecewise linear interface calculation (PLIC). Among them, the PLIC method can provide higher accuracy, smaller diffusion effect and better conservation than the SLIC method.

[0005] In contrast, although the algebraic VOF method can also effectively track the fluid interface, it may produce large diffusion at the interface, causing the interface contour to become blurred. In addition, in practical engineering problems, the geometry of the flow area is usually very complex, and using unstructured grids for spatial discretization is more flexible and practical than structured grids.

[0006] In order to meet the needs of fluid interface tracking on unstructured grids, existing technologies need to develop VOF methods suitable for such grids. The core steps of the VOF method include interface reconstruction and interface advancement. In the interface reconstruction stage, there are two commonly used methods: one is to determine the optimal interface normal vector based on the least squares method; the other is to use the height function method to calculate the interface normal vector and curvature. However, in unstructured grids, due to the irregular shape of the control body, the calculation of the volume flux of the fluid flowing through the surface of the control body becomes complicated, and usually needs to be implemented through iterative calculation or block accumulation, which increases the complexity of the algorithm and reduces the code development speed and execution efficiency.

[0007] Therefore, in response to the above dilemma, how to develop a new fluid interface tracking method suitable for unstructured grids has become the key for technical personnel in this field to conduct relevant research. Summary of the invention

[0008] Based on the current status of the background technology, the purpose of the present invention is to solve the problems of complex iterative calculation and low efficiency when the existing methods are applied to fluid interface tracking. Therefore, a three-dimensional fluid interface tracking method for unstructured grid finite volume method is proposed. The present invention combines the variational method with the VOF method to track the fluid interface, thereby determining the optimal fluid interface normal direction; at the same time, through a new fluid volume flux solution method, no iterative calculation is required when solving the fluid volume flux, and the solution is fast and efficient, so that the numerical simulation results have good mass conservation.

[0009] The present invention adopts the following technical solutions to achieve the purpose:

[0010] A three-dimensional fluid interface tracking method for an unstructured grid finite volume method, when the method uses a VOF method to track the three-dimensional fluid interface, for multiple control bodies in an unstructured grid, a variational method is combined with the VOF method to determine the optimal fluid interface normal direction; in the variational method, the fluid volume fraction of a certain control body is used to calculate the fluid volume fraction of its adjacent control body according to the Taylor formula and a target functional, and the target functional is defined as: the sum of the absolute values ​​of the differences between the fluid volume fractions of all control bodies adjacent to a certain control body calculated by the Taylor formula and the current actual fluid volume fraction; by calculating the target functional, the optimal fluid interface normal direction of the current control body is obtained, thereby completing the three-dimensional fluid interface tracking.

[0011] Specifically, the steps of using the VOF method to track a three-dimensional fluid interface are as follows:

[0012] S1. Initialization of calculation parameters; the calculation parameters include calculation grid, physical quantity and initial fluid volume fraction distribution information;

[0013] S2. Reconstruct the fluid interface; select the grid containing the fluid interface in the calculation domain, solve the normal direction of the fluid interface based on the variational method, calculate the slope parameters of the fluid interface, and finally update the interface field data;

[0014] S3, perform fluid interface advancement; first initialize the surface volume flow rate, then calculate the surface volume flow rate within the time step, then calculate the net volume flow rate of each control volume, and finally update the control volume fraction of the fluid;

[0015] S4. updating the density and viscosity of the flow field according to the updated control volume fraction of the fluid;

[0016] S5. Use the updated flow field density and viscosity to perform flow field calculation;

[0017] S6. Enter the calculation of the next time step and repeat the process from step S2 to step S5 until the end condition is met.

[0018] When calculating the volume flow rate of the surface in the time step in step S3, that is, calculating the volume flow rate flowing through the control body surface per unit time Fluid volume flux The calculation of this parameter adopts a non-iterative and explicit calculation method to achieve a faster and more efficient solution process.

[0019] In summary, due to the adoption of this technical solution, the beneficial effects of the present invention are as follows:

[0020] The present invention can accurately track the movement and deformation of the fluid interface, especially in complex unstructured grids, and can effectively reduce the fuzziness and diffusion of the interface, thereby improving the accuracy of the simulation results. The method uses a variational approach to determine the optimal interface normal direction, which not only improves the computational efficiency, but also ensures that the normal direction of the fluid interface is more accurate, which helps to more accurately describe the geometric characteristics of the interface.

[0021] The present invention also adopts a non-iterative, explicit fluid volume flux calculation method, which does not require a complex iterative process, significantly improves the calculation speed, simplifies program design, and is conducive to the rapid development and deployment of software. Through improved interface tracking and fluid volume flux calculation methods, the present invention ensures the conservation of mass near the fluid interface, which is crucial to maintaining the physical meaning of the simulation results.

[0022] The present invention is applicable to various complex gas-liquid two-phase flow numerical simulation scenarios, especially those involving unstructured grids, and can effectively deal with complex flow area geometries in practical engineering problems. The application of this method is easy to implement, does not require extremely complex mathematical tools in the field, reduces the difficulty of programming, and is convenient for scientific researchers and technicians to quickly master and apply. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Detailed diagram of the complete process of the unstructured grid three-dimensional fluid interface tracking method. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the parts of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0025] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] Example

[0027] A three-dimensional fluid interface tracking method for unstructured grid finite volume method, the key of the method is: when using VOF method to track the three-dimensional fluid interface, for multiple control bodies in the unstructured grid, the variational method is combined with the VOF method to determine the best fluid interface normal direction; in the variational method, according to Taylor formula and target functional, the fluid volume fraction of a certain control body is used to calculate the fluid volume fraction of its adjacent control body, and the target functional is defined as: the sum of the absolute values ​​of the differences between the fluid volume fractions calculated by Taylor formula of all control bodies adjacent to a certain control body and the current actual fluid volume fraction; by calculating the target functional, the best fluid interface normal direction of the current control body is obtained, and the three-dimensional fluid interface tracking is completed.

[0028] like Figure 1 As shown, this embodiment introduces the detailed process of unstructured grid three-dimensional fluid interface tracking using the above method process, that is, the steps of three-dimensional fluid interface tracking using the VOF method are as follows:

[0029] S1. Initialization of calculation parameters; the calculation parameters include the required calculation grid, physical quantities (velocity, pressure, etc.) and initial fluid volume fraction distribution information;

[0030] S2. Reconstruct the fluid interface; select the grid containing the fluid interface in the calculation domain, solve the normal direction of the fluid interface based on the variational method, calculate the slope parameters of the fluid interface, and finally update the interface field data;

[0031] S3, perform fluid interface advancement; first initialize the surface volume flow rate, then calculate the surface volume flow rate within the time step, then calculate the net volume flow rate of each control volume, and finally update the control volume fraction of the fluid;

[0032] S4. updating the density and viscosity of the flow field according to the updated control volume fraction of the fluid;

[0033] S5, using the updated flow field density and viscosity, solving the NS equation to perform flow field calculation;

[0034] S6. Enter the calculation of the next time step and repeat the process from step S2 to step S5 until the end condition is met.

[0035] Based on the above method flow, the key points of this embodiment are the process of solving the normal direction of the fluid interface based on the variational method in step S2 and the process of calculating the internal volume flow rate of the time step in step S3.

[0036] This embodiment combines the variational method with the VOF method to track the fluid interface. The variational method is mainly used to determine the direction of the optimal fluid interface normal. Since the fluid interface is continuous, the fluid volume fraction is also continuous on the fluid interface. According to Taylor's formula, the control volume is used The volume fraction of the fluid Calculate its adjacent control volume The volume fraction of the fluid , the calculation formula is as follows:

[0037]

[0038] In the formula, , and Respectively represent the control body With control body Between , and Coordinate differences in three directions; , and They represent the unit vectors of the fluid interface normal. , and Components in three directions; represents a second-order small quantity.

[0039] The control body The volume fraction of the fluid The second-order small quantity is omitted in the calculation formula, and the new calculation formula is as follows:

[0040]

[0041] The above formula is used to define the target functional The volume fraction of the fluid .

[0042] In this embodiment, the control body All adjacent control volumes The total number is recorded as , while As a serial number to represent the control body The adjacent After the control volume, the objective functional Defined as: Control volume All adjacent control bodies Taylor's formula for calculating fluid volume fraction With the current control body The actual fluid volume fraction The sum of the absolute values ​​of the differences is defined as follows:

[0043]

[0044] The target functional The value of is constrained to the corresponding minimum value, as follows:

[0045]

[0046] The adjacent fluid volume fraction is obtained Piecewise smooth polynomial in the computational domain and use it as the current control volume The optimal solution for the normal direction of the fluid interface.

[0047] The above is a detailed description of the process of solving the normal direction of the fluid interface based on the variational method in step S2. Next, the process of calculating the internal volume flow rate of the time step in step S3 is further described in detail in this embodiment.

[0048] For gas-liquid two-phase flow, the VOF method uses the fluid volume fraction It represents the volume fraction of liquid in the grid, as follows:

[0049]

[0050] In the formula, when When , it means the grid is full of gas; when When , it means the grid is filled with liquid; when , it means that part of the grid is filled with liquid, that is, there is an interface where gas and liquid intersect in the grid.

[0051] In the VOF method, the fluid volume fraction The transport equation is as follows:

[0052]

[0053] In the formula, represents the velocity vector, represents time; through the finite volume method, the above transport equation is spatially integrated over the control volume, combined with the divergence theorem, and written as the following integral form:

[0054]

[0055] In the formula, represents the number of time steps, represents the time step (i.e., from arrive The time interval of the time step), represents the volume of the control volume, Represents the unit vector of the normal direction of the control body surface; Represents the surface integration of the control volume; different time steps are realized by the above formula Calculate the fluid volume fraction of each control volume under .

[0056] For the time step , the total mass of liquid in the computational domain is as follows:

[0057]

[0058] In the formula, represents the total mass of the liquid, represents the total number of control bodies, Represents the time step Time The mass of the control volume, Indicates The fluid volume fraction of the control volume, Indicates The volume of a control volume;

[0059] For the time step , the total mass of liquid in the computational domain is as follows:

[0060]

[0061] In the formula, Indicates The control body from arrive The mass added during the time step; Calculation of the mass increment of each control volume to achieve the fluid volume fraction The calculation of mass increment is described as follows.

[0062] from arrive When the control volume of the time step is filled with the same fluid, the mass of the control volume remains unchanged according to the incompressible flow property. The control volume is the control volume with the fluid interface, and its mass increment is calculated by summing the fluid volume flux on each surface of the control volume, as follows:

[0063]

[0064] In the formula, Indicates the ordinal number of the control face, represents the total number of control faces, The time change represented by arrive The time interval between time steps; Represents the flow through the control surface per unit time The volume flux of the fluid.

[0065] In unstructured networks, due to the irregular geometry of the control body, the solution of the fluid volume flux flowing through the control body surface is often carried out by iterative calculation or block accumulation. These methods are complex and not conducive to code development and fast solution. Therefore, in this embodiment, a new calculation formula is used to solve the fluid volume flux, that is, the volume of fluid flowing through the control body surface per unit time. Fluid volume flux , the calculation formula is as follows:

[0066]

[0067] In the formula, Indicates control The normal velocity at Indicates control The area of represents the unit vector of the normal direction outside the fluid interface, represents the unit vector of the external normal direction of the control volume surface, It means to solve the absolute value;

[0068] In the formula, The first part is used to calculate the equivalent velocity, and the other parts except this part are used to calculate the equivalent area.

[0069] The solution of this calculation formula does not require iterative calculation, and based on the above method process, the solution calculation is an explicit calculation, so the solution is fast and efficient, and it is also easy to program.

Claims

1. A three-dimensional fluid interface tracking method for unstructured grid finite volume method, characterized by: When the VOF method is used for three-dimensional fluid interface tracking, the variational method is combined with the VOF method for multiple control bodies in the unstructured grid to determine the optimal fluid interface normal direction; in the variational method, the fluid volume fraction of a certain control body is used to calculate the fluid volume fraction of its adjacent control body according to the Taylor formula and the target functional, and the target functional is defined as: the sum of the absolute values ​​of the differences between the fluid volume fractions calculated by the Taylor formula of all control bodies adjacent to a certain control body and the current actual fluid volume fraction; by calculating the target functional, the optimal fluid interface normal direction of the current control body is obtained, thereby completing the three-dimensional fluid interface tracking; According to Taylor's formula, using the control volume The volume fraction of the fluid Calculate its adjacent control volume The volume fraction of the fluid , the calculation formula is as follows: In the formula, , and Respectively represent the control body With control body Between , and Coordinate differences in three directions; , and They represent the unit vectors of the fluid interface normal. , and Components in three directions; represents a second-order small quantity; The control body All adjacent control volumes The total number is recorded as , while As a serial number to represent the control body The adjacent After the control volume, the objective functional Defined as: Control volume All adjacent control bodies Taylor's formula for calculating fluid volume fraction With the current control body The actual fluid volume fraction The sum of the absolute values ​​of the differences is defined as follows: The target functional The value of is constrained to the corresponding minimum value, as follows: The adjacent fluid volume fraction is obtained Piecewise smooth polynomial in the computational domain and use it as the current control volume The optimal solution for the normal direction of the fluid interface; The steps for 3D fluid interface tracking using the VOF method are as follows: S1. Initialization of calculation parameters; the calculation parameters include calculation grid, physical quantity and initial fluid volume fraction distribution information; S2. Reconstruct the fluid interface; select the grid containing the fluid interface in the calculation domain, solve the normal direction of the fluid interface based on the variational method, calculate the slope parameters of the fluid interface, and finally update the interface field data; S3, perform fluid interface advancement; first initialize the surface volume flow rate, then calculate the surface volume flow rate within the time step, then calculate the net volume flow rate of each control volume, and finally update the control volume fraction of the fluid; S4. updating the density and viscosity of the flow field according to the updated control volume fraction of the fluid; S5. Use the updated flow field density and viscosity to perform flow field calculation; S6, enter the calculation of the next time step, and repeat the process from step S2 to step S5 until the end condition is met; For gas-liquid two-phase flow, the VOF method uses the fluid volume fraction It represents the volume fraction of liquid in the grid, as follows: In the formula, when When , it means the grid is full of gas; when When , it means the grid is filled with liquid; when When , it means that part of the grid is filled with liquid, that is, there is an interface where gas and liquid intersect in the grid; Fluid volume fraction The transport equation is as follows: In the formula, represents the velocity vector, represents time; through the finite volume method, the above transport equation is spatially integrated over the control volume, and combined with the divergence theorem, it is written as the following integral form: In the formula, represents the number of time steps, represents the time step, represents the volume of the control volume, Represents the unit vector of the normal direction of the control body surface; Represents the surface integration of the control volume; different time steps are realized by the above formula Calculate the fluid volume fraction of each control volume under ; For the time step , the total mass of liquid in the computational domain is as follows: In the formula, represents the total mass of the liquid, represents the total number of control bodies, Represents the time step Time The mass of the control volume, Indicates The fluid volume fraction of the control volume, Indicates The volume of a control volume; For the time step , the total mass of liquid in the computational domain is as follows: In the formula, Indicates The control body from arrive The mass added during the time step; Calculation of the mass increment of each control volume to achieve the fluid volume fraction Updates to perform three-dimensional fluid interface tracking; The first time the quality increase occurs The control volume is a control volume with a fluid interface, and its mass increment is calculated by summing the fluid volume flux on each surface of the control volume, as follows: In the formula, Indicates the ordinal number of the control face, represents the total number of control faces, The time change represented by arrive The time interval between time steps; Represents the flow through the control surface per unit time The volume flux of the fluid; Flow through the control surface per unit time Fluid volume flux The calculation formula is as follows: In the formula, Indicates control The normal velocity at Indicates control The area of represents the unit vector of the normal direction outside the fluid interface, represents the unit vector of the external normal direction of the control volume surface, It means to solve the absolute value; In the formula, The first part is used to calculate the equivalent velocity, and the other parts except this part are used to calculate the equivalent area.

2. The three-dimensional fluid interface tracking method for unstructured grid finite volume method according to claim 1, characterized in that: The control body The volume fraction of the fluid The second-order small quantity is omitted in the calculation formula, and the new calculation formula is as follows: The above formula is used to define the target functional The volume fraction of the fluid .

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