A method, system and related devices for determining flow field parameters of a compressible two-phase flow

Abstract

This application discloses a method, system, and related apparatus for determining the flow field parameters of compressible two-phase flow, belonging to the technical field of two-phase flow analysis. The method for determining the flow field parameters of compressible two-phase flow includes: dividing the target flow field into multiple tetrahedral elements and initializing the target flow field; determining the flow control equations of the target flow field and performing spatial and temporal discretization operations on the flow control equations; solving the flow control equations after spatial and temporal discretization operations; processing the interface elements using a real virtual fluid method to generate the flow field information of the target flow field at the next time step; and solving the discretized VOF transport equations to determine the two-phase flow interface of the target flow field at the next time step. This application can reduce the number of iterations and computational load in determining the flow field parameters of compressible two-phase flow, and improve the conservation properties in the calculation of compressible two-phase flow.

Description

Technical Field

[0001] This application relates to the field of two-phase flow analysis technology, and in particular to a method, system and related apparatus for determining flow field parameters of compressible two-phase flow. Background Technology

[0002] Two-phase flow is a research hotspot in computational fluid dynamics. Compressible two-phase flow plays an important role in many fields, such as underwater ignition of missiles, underwater explosions, and supercavitation of high-speed underwater vehicles, all of which require analysis of the flow field parameters of compressible two-phase flow.

[0003] Currently, the level-set method is mainly used in related technologies to capture interfaces and determine flow field parameters. Although this method can capture discontinuities well, its conservation is poor. After multiple iterations, it often causes large volume losses. Moreover, the level-set function needs to be re-initialized after each iteration, resulting in a large amount of computation. If the interface breaks or merges during the calculation, the level-set method is difficult to capture accurately.

[0004] Therefore, how to reduce the number of iterations and computational load in determining the flow field parameters of compressible two-phase flow, and improve the conservation in the calculation of compressible two-phase flow, is a technical problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] The purpose of this application is to provide a method for determining the flow field parameters of a compressible two-phase flow, a system for determining the flow field parameters of a compressible two-phase flow, a storage medium, and an electronic device, which can reduce the number of iterations and computational load in determining the flow field parameters of a compressible two-phase flow and improve the conservation of flow field parameters in the calculation of a compressible two-phase flow.

[0006] To address the aforementioned technical problems, this application provides a method for determining the flow field parameters of a compressible two-phase flow, the method comprising:

[0007] Step 1: Determine the target flow field when the target object moves in a compressible two-phase fluid;

[0008] Step 2: Divide the target flow field into multiple tetrahedral elements, and initialize the target flow field at T. n Flow field information and volume fraction at any given time;

[0009] Step 3: Determine the flow control equations for the target flow field, and perform spatial and temporal discretization operations on the flow control equations;

[0010] Step 4: Solve the flow control equations obtained after the spatial and temporal discretization operations to obtain the flow control equations at time T. nThe flux on the control surface of the non-interface unit at time T; wherein, the non-interface unit is not in the target flow field at time T n Tetrahedral elements at the interface between two phases at a given time;

[0011] Step 5: Process the interface elements using a realistic virtual fluid method and solve for the T... n The flux on the control surface of the interface unit at time T; wherein, the interface unit is located in the target flow field at time T n Tetrahedral elements at the interface between two phases at a given time;

[0012] Step 6: Based on T n The flux generated on the control surface of the non-interface unit and the interface unit at time T generates the target flow field. n+1 Flow field information at any given moment;

[0013] Step 7: Solve the discretized VOF transport equations to obtain the values ​​of all the tetrahedral elements at T. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1 The interface between the two phases at a given moment;

[0014] Step 8: Determine if the iteration termination condition has been met; if so, output the given T. n+1 The flow field information at time T and the T n+1 The two-phase flow interface at time n; if not, increment the value of n by 1 and proceed to step 4.

[0015] Optionally, the flow control equations are subjected to spatial and temporal discretization operations, including:

[0016] The flow control equations are spatially discretized using the finite volume method.

[0017] The flow control equations are discretized in time using the second-order Runge-Kutta method.

[0018] Optionally, the flow control equations obtained after the spatial and temporal discretization operations are solved to obtain the flow control equations at time T. n The flux on the control surface of the non-interface unit at any given time includes:

[0019] The flow control equations, after the spatial and temporal discretization operations, are solved using the AUSM+-UP method to obtain the flow control equations at time T. n The flux on the control surface of the non-interface unit at that moment.

[0020] Optionally, the interface unit is processed using a real virtual fluid method, and the solution is obtained at T. nThe flux on the control surface of the interface unit at any given time includes:

[0021] The interface unit is subjected to interface boundary processing using a real virtual fluid method, and the flux on the control surface of the interface unit is solved using the interface boundary processing results.

[0022] Optionally, solving the discretized VOF transport equation yields all the tetrahedral elements at T. n+1 The volume fraction and interface normal vector at time step 1 include:

[0023] The volume flux of the control surface of the tetrahedral element is obtained by solving the discretized VOF transport equation.

[0024] The volume flux of the tetrahedral element at T is calculated based on the volume flux of the control surface of the tetrahedral element. n+1 Volume fraction at time;

[0025] According to the tetrahedral unit at T n+1 The volume fraction at time T is obtained by solving the equation for the tetrahedral element at time T. n+1 The interface normal vector at time t.

[0026] Optionally, determining whether the iteration termination condition has been met includes:

[0027] Determine T n Is the time the preset time? (T) n+1 With T n The difference is the iteration period;

[0028] If so, then the iteration termination condition is determined to have been met;

[0029] If not, then the iteration termination condition has not been met.

[0030] Optionally, determining the target flow field when the target object moves in a compressible two-phase fluid includes:

[0031] Determine the target flow field when a propeller moves in a compressible two-phase fluid; wherein the compressible two-phase fluid is water and air.

[0032] Accordingly, in the output of T n+1 The flow field information at time T and the T n+1 Following the two-phase flow interface at a given time, it also includes:

[0033] According to the T n+1 The flow field information at time T and the T n+1 The mechanical damage level of the propeller is calculated at the two-phase flow interface at a given time.

[0034] The propeller blade shape is adjusted according to the level of mechanical damage.

[0035] This application also provides a system for determining the flow field parameters of a compressible two-phase flow, the system comprising:

[0036] The flow field determination module is used to determine the target flow field when a target object moves in a compressible two-phase fluid;

[0037] An initialization module is used to divide the target flow field into multiple tetrahedral elements and initialize the target flow field at T. n Flow field information and volume fraction at any given time;

[0038] The discrete processing module is used to determine the flow control equations of the target flow field and to perform spatial and temporal discretization operations on the flow control equations.

[0039] The first flux determination module is used to solve the flow control equations after the spatial discretization operation and the time discretization operation, and obtain the flux determination at time T. n The flux on the control surface of the non-interface unit at time T; wherein, the non-interface unit is not in the target flow field at time T n Tetrahedral elements at the interface between two phases at a given time;

[0040] The second flux determination module is used to process the interface elements using a realistic virtual fluid method and solve for the flux at T. n The flux on the control surface of the interface unit at time T; wherein, the interface unit is located in the target flow field at time T n Tetrahedral elements at the interface between two phases at a given time;

[0041] The flow field information update module is used to update the flow field information based on the flow field information at T. n The flux generated on the control surface of the non-interface unit and the interface unit at time T generates the target flow field. n+1 Flow field information at any given moment;

[0042] The interface update module is used to solve the discretized VOF transport equation to obtain the interface update of all the tetrahedral elements at T. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1 The interface between the two phases at a given moment;

[0043] The iteration judgment module is used to determine whether the iteration termination condition has been met; if so, it outputs the T value. n+1 The flow field information at time T and the T n+1 The two-phase flow interface at time n; if not, increment the value of n by 1 and proceed to the processing flow of the discrete processing module.

[0044] This application also provides a storage medium storing a computer program thereon, which, when executed, implements the steps of the above-described method for determining the flow field parameters of a compressible two-phase flow.

[0045] This application also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the above-described method for determining the flow field parameters of a compressible two-phase flow.

[0046] This application provides a method for determining the flow field parameters of a compressible two-phase flow, comprising: Step 1: determining the target flow field when a target object moves in a compressible two-phase fluid; Step 2: dividing the target flow field into multiple tetrahedral elements and initializing the target flow field at T n Step 3: Determine the flow control equations for the target flow field, and perform spatial and temporal discretization operations on the flow control equations; Step 4: Solve the flow control equations after the spatial and temporal discretization operations to obtain the flow field information and volume fraction at time T. n The flux on the control surface of the non-interface unit at time T; wherein, the non-interface unit is not in the target flow field at time T ni Step 5: Process the interface elements at time T using a real virtual fluid method and solve for the two-phase flow interface. n The flux on the control surface of the interface unit at time T; wherein, the interface unit is located in the target flow field at time T n Tetrahedral elements of the two-phase flow interface at time T; Step 6: Based on T n The flux generated on the control surface of the non-interface unit and the interface unit at time T generates the target flow field. n+1 Flow field information at time T; Step 7: Solve the discretized VOF transport equation to obtain the flow field information of all the tetrahedral elements at time T. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1 The two-phase flow interface at time T; Step 8: Determine if the iteration termination condition has been met; if so, output the T value. n+1 The flow field information at time T and the T n+1 The two-phase flow interface at time n; if not, increment the value of n by 1 and proceed to step 4.

[0047] This application, after determining the target flow field of the target object moving in a compressible two-phase fluid, divides the target flow field into multiple tetrahedral elements and initializes the target flow field. After initializing the target flow field, this application determines the flow field information and the two-phase interface at each time step through iterative calculation. During the iteration process, this application solves the flow control equations after spatial and temporal discretization operations to obtain the flow field information at time T. n The flux on the control surface of the non-interface element at time T; this application also processes the interface element and solves for the flux at time T using a real virtual fluid method. n The flux on the control surface of the interface unit at time T is used to obtain the target flow field at time T. n+1 In addition to obtaining the flow field information at time T, this application also solves the discretized VOF transport equation to obtain the flow field information of all the tetrahedral elements at time T. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1 The interface between the two phases at a given time. The iterative process described above combines the VOF method with the real-virtual flow method to solve for compressible two-phase flows. Compared to compressible two-phase flow algorithms based on the Level-set method in related technologies, this application simplifies the calculation process and improves the ability to handle interface fusion and interface fragmentation. Therefore, this application can reduce the number of iterations and computational load for determining the flow field parameters of compressible two-phase flows, and improve the conservation of laws in compressible two-phase flow calculations. This application also provides a system for determining the flow field parameters of compressible two-phase flows, a storage medium, and an electronic device, which have the above-mentioned beneficial effects, and will not be elaborated further here. Attached Figure Description

[0048] To more clearly illustrate the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 A flowchart illustrating a method for determining flow field parameters of a compressible two-phase flow provided in an embodiment of this application;

[0050] Figure 2 This is a schematic diagram illustrating a high-order format construction provided in an embodiment of this application;

[0051] Figure 3 This is a schematic diagram illustrating the solution of the VOF interface normal provided in an embodiment of this application;

[0052] Figure 4 A schematic diagram illustrating the classification of interface units provided in an embodiment of this application;

[0053] Figure 5 This is a schematic diagram of an interface volume flux calculation provided in an embodiment of this application;

[0054] Figure 6 A schematic diagram illustrating the establishment of boundary conditions at a two-phase flow interface provided in an embodiment of this application;

[0055] Figure 7 This is a schematic diagram of a virtual fluid structure provided in an embodiment of this application;

[0056] Figure 8 A schematic diagram illustrating the interface capture effect after spherical deformation recovery, provided in an embodiment of this application.

[0057] Figure 9 A schematic diagram illustrating the interface capture effect of spherical shear deformation provided in an embodiment of this application;

[0058] Figure 10 This is a comparison chart of numerical results and exact solutions for a water vapor shock tube in the density dimension, provided in an embodiment of this application.

[0059] Figure 11 This is a comparison chart of numerical results and exact solutions for a water vapor shock tube in the pressure dimension provided in an embodiment of this application.

[0060] Figure 12 This is a comparison chart of numerical results and exact solutions for a water vapor shock tube in the velocity dimension, provided in an embodiment of this application.

[0061] Figure 13 An isosurface diagram of the interface between a shock wave and a helium bubble, provided in an embodiment of this application;

[0062] Figure 14 This is a symmetrical cross-sectional density cloud map of the interaction between a shock wave and a helium bubble, provided as an embodiment of this application. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0064] Please see below. Figure 1 , Figure 1 This is a flowchart illustrating a method for determining flow field parameters of a compressible two-phase flow, as provided in an embodiment of this application.

[0065] Specific steps may include:

[0066] S101: Determine the target flow field when the target object moves in a compressible two-phase fluid;

[0067] This embodiment can be applied to computers with fluid dynamics calculation capabilities. The target object can be a missile, propeller, aircraft, or similar object. The compressible two-phase fluid is a flow system composed of two compressible fluids, including a primary phase fluid and a secondary phase fluid. The fluids in the compressible two-phase fluid can be any two of the following compressible fluids: water, air, nitrogen, oxygen, carbon dioxide, gasoline, liquid metal, etc.

[0068] When the target object moves in the above-mentioned compressible two-phase fluid, a compressible two-phase flow field is formed. This application can select the compressible two-phase flow field of the above-mentioned specific region as the target flow field.

[0069] S102: Divide the target flow field into multiple tetrahedral elements, and initialize the target flow field at T n Flow field information and volume fraction at any given time;

[0070] In this embodiment, after determining the target flow field, the target flow field can be divided into multiple tetrahedral elements. As a feasible implementation method, this embodiment can divide the target flow field into multiple tetrahedral elements of the same shape and size.

[0071] This embodiment can also initialize the target flow field at T. n The flow field information and volume fraction at any given time are as follows: the flow field information includes density, pressure, velocity, etc.; the volume fraction describes the flow field properties (primary phase fluid or secondary phase fluid) of the tetrahedral element; and the flow field properties describe whether the tetrahedral element corresponds to the primary phase fluid or the secondary phase fluid. The flow field information and volume fraction are collectively referred to as flow field parameters.

[0072] As a feasible implementation method, this embodiment can determine T by the target object's velocity and the environmental flow field parameters of the compressible two-phase fluid. n The initial value of the target flow field at time T is determined, and then the target flow field is initialized based on the above initial value at time T. n The flow field information and volume fraction at time t. Here, 'n' represents the sequence number of the update time, and 'T' represents the initial flow field information and volume fraction. n The time is the initial time T1.

[0073] The target flow field mentioned above includes a primary phase fluid and a secondary phase fluid. In this embodiment, the flow field information is initialized, that is, the flow field information (such as velocity, density, and pressure) is assigned to each tetrahedral element, and the volume fraction of each element is assigned. The volume fraction of the primary phase fluid is assigned a value of 1, the volume fraction of the secondary phase fluid is assigned a value of 0, and the remaining flow field information is given according to the actual values ​​of the flow field at the location of the tetrahedral element at the initial moment.

[0074] S103: Determine the flow control equations of the target flow field, and perform spatial and temporal discretization operations on the flow control equations;

[0075] In this embodiment, the Euler equation can be selected as the flow control equation for the target flow field. Then, spatial and temporal discretization operations are performed on the flow control equation, thereby converting the solution of the flow control equation into the solution of the flux on the unit control surface.

[0076] S104: Solve the flow control equations after the spatial and temporal discretization operations to obtain the flow control equations at time T. n Flux on the control surface of a non-interface unit at any given moment;

[0077] This embodiment can determine the two-phase flow interface of the target flow field, and then solve the flow control equations after spatial and temporal discretization operations to obtain the flow control equations at time T. n The flux on the control surface of a non-interface element at any given time. The two-phase flow interface mentioned above is the interface between the primary phase fluid and the secondary phase fluid in the target flow field. The control surface refers to the face of a tetrahedral element, and the flux on the control surface includes velocity flux, density flux, pressure flux, etc.

[0078] Specifically, in this embodiment, the flow control equations after the spatial and temporal discretization operations can be solved using the AUSM+-UP method to obtain the flow control equations at time T. n The flux on the control surface of the non-interface unit at the specified time. The AUSM+-UP method is an improvement on the upwind vector flux splitting scheme (AUSM), which adds a dissipation term to the traditional AUSM scheme.

[0079] The tetrahedral elements in the target flow field include non-interface elements and interface elements. Non-interface elements are those not located within the target flow field at time T. n The tetrahedral element of the two-phase flow interface at time T; the interface element is located in the target flow field at time T n The tetrahedral element of the interface between the two-phase flow at time T. In this embodiment, the interface element can be determined based on the flow field properties, and the flow control equations after spatial and temporal discretization can be solved to obtain T. n The flux on the control surface of the non-interface unit in the target flow field at the specified time.

[0080] S105: Process the interface elements using a realistic virtual fluid method and solve for the T... n The flux on the control surface of the interface unit at any given time;

[0081] In this step, the interface elements in the target flow field are processed using a realistic virtual fluid method, and then the flux of the control surface of the interface elements is solved to obtain the flux at T. n The flux on the control surface of the interface unit at any given time. Specifically, in this embodiment, the interface boundary of the interface unit can be processed using a real virtual fluid method, and the flux on the control surface of the interface unit can be solved using the interface boundary processing result.

[0082] S106: According to T n The flux generated on the control surface of the non-interface unit and the interface unit at time T generates the target flow field. n+1 Flow field information at any given moment;

[0083] T has already been solved n Based on the flux of the control surface of the non-interface unit at a given time, it can be combined with T n The flux on the control surface of the interface unit at time T is obtained. n The flux of all tetrahedral elements in the target flow field at time T, and then according to T n The flux of all tetrahedral elements in the target flow field at time T is used to obtain the entire flow field at time T. n+1 Flow field information at any given time. T n+1 The moment is T n The next moment after time, T n+1 Time and T n The time difference is the iteration period of the flow field parameters (e.g., 1 millisecond or 10 milliseconds).

[0084] The flow field information can be updated through operations S104, S105, and S106, that is: T n The flow field information at time T is updated. n+1 Flow field information at any given moment.

[0085] S107: Solve the discretized VOF transport equation to obtain the T values ​​of all the tetrahedral elements. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1 The interface between the two phases at a given moment;

[0086] Prior to this step, the target flow field can also be measured at T. nDiscretizing the VOF transport equation at time t is used to obtain the discrete form of the VOF transport equation, thus transforming the solution of the VOF transport equation into the solution of the volume flux through each control surface of the cell.

[0087] This step allows us to solve the discretized VOF transport equations to obtain the values ​​of all the tetrahedral elements at T. n+1 The volume fraction and interface normal vector at time t. Specifically, this step can solve for the volume flux of the control surface, and obtain T based on the volume flux solution. n+1 The volume fraction of each tetrahedral element at time step T is determined, and then the interface normal vector within the interface element is calculated based on the volume fraction of each tetrahedral element. Finally, T is reconstructed based on the interface normal vector and volume fraction within the interface element. n+1 The interface between two phases at a given moment (i.e., the interface between two fluids).

[0088] The operation of S107 enables the updating of the two-phase flow interface, that is: changing T n The two-phase flow interface at time T is updated. n+1 The interface between the two phases at a given moment.

[0089] S108: Determine whether the iteration termination condition has been met; if yes, proceed to step S109; if no, increment the value of n by 1 and proceed to S104.

[0090] This step determines whether the current iteration state has reached the iteration termination condition, which can be a time-based termination condition or a count-based termination condition. Specifically, this embodiment determines the time T corresponding to the currently updated flow field information and the two-phase flow interface. n Is it a preset time (or later than a preset time)? If yes, then the current iteration state is determined to have reached the iteration termination condition; if no, then the current iteration state is determined not to have reached the iteration termination condition. This embodiment can determine whether the currently updated flow field information and the number of iterations of the two-phase flow interface are a preset number (or greater than a preset number); if yes, then the current iteration state is determined to have reached the iteration termination condition; if no, then the current iteration state is determined not to have reached the iteration termination condition.

[0091] Specifically, if the iteration termination condition is not met, this embodiment can determine the flow field properties of each element after the solution (i.e., whether it belongs to the main phase fluid or the secondary phase fluid) based on the volume fraction value obtained in the solution.

[0092] S109: Output the T n+1 The flow field information at time T and the T n+1 The interface between the two phases at a given moment;

[0093] Among them, in obtaining T n+1After obtaining the flow field information and the two-phase flow interface at a given time, this embodiment can use the above flow field information and the two-phase flow interface to analyze the motion state of the target object and obtain the motion state analysis results of the target object.

[0094] Specifically, in the scenario of underwater gas jets from a missile (i.e., the target object is a missile), gas bubbles will be generated in the water (at this time, the compressible two-phase fluid includes water and gas bubbles). The complex wave system structure inside the gas bubbles can lead to accidents such as pressure oscillations. In this embodiment, the change information of the gas bubbles can be determined based on the flow field information obtained through iteration and the interface between the two phases, and then the missile can be adjusted accordingly based on the above change information (such as adjusting the depth of the missile when it is ignited and launched underwater).

[0095] In the underwater vehicle scenario (i.e., the target object is a vehicle), drag can be reduced by active ventilation (in which case the compressible two-phase fluid includes water and air bubbles). In this embodiment, the distribution information of air bubbles surrounding the vehicle can be determined based on the flow field information obtained through iteration and the interface between the two phases, and then the ventilation volume of the vehicle can be adjusted according to the distribution information.

[0096] In a scenario where a ship navigates water using a propeller (i.e., the target object is the propeller), small bubbles are generated around the propeller as it rotates and quickly collapse (at this time, the compressible two-phase fluid includes water and bubbles). This situation can cause mechanical damage to the propeller. This embodiment can determine the damage level of the propeller based on the iteratively obtained flow field information and the interface between the two phases, thereby optimizing the propeller blade shape. Specifically, this embodiment can determine the target flow field when the propeller moves in a compressible two-phase fluid; wherein, the compressible two-phase fluid is water and air; and the output T... n+1 The flow field information at time T and the T n+1 After the two-phase flow interface at time T, it can also be based on the stated T n+1 The flow field information at time T and the T n+1 The mechanical damage level of the propeller is calculated at the two-phase flow interface at a given time; the propeller blade shape is adjusted according to the mechanical damage level. The aforementioned mechanical damage level describes the degree of damage to the propeller caused by the compressible two-phase fluid. In this embodiment, the blade shape corresponding to each mechanical damage level can be preset, and the propeller blade shape can be adjusted based on the above correspondence. Specifically, in this embodiment, the propeller blade shape can be adjusted in the propeller design file so that the propeller can be manufactured according to the design file.

[0097] In this embodiment, after determining the target flow field of the target object moving in a compressible two-phase fluid, the target flow field is divided into multiple tetrahedral elements and initialized. After initializing the target flow field, this embodiment determines the flow field information and the two-phase interface at each time step through iterative calculation. During the iteration process, this embodiment solves the flow control equations after spatial and temporal discretization operations to obtain the flow field information at time step T. n The flux on the control surface of the non-interface element at time T; this embodiment also processes the interface element and solves for the flux at time T using a real virtual fluid method. n The flux on the control surface of the interface unit at time T is used to obtain the target flow field at time T. n+1 In this embodiment, the flow field information at time T is obtained by solving the discretized VOF transport equations. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1 The interface between the two phases at a given time. The iterative process described above combines the VOF method with the real-virtual flow method to solve for compressible two-phase flows. Compared to compressible two-phase flow algorithms based on the Level-set method in related technologies, this embodiment simplifies the calculation process and improves the ability to handle interface fusion and interface fragmentation. Therefore, this embodiment can reduce the number of iterations and computational load for determining the flow field parameters of compressible two-phase flows, and improve the conservation properties in the calculation of compressible two-phase flows.

[0098] As for Figure 1 Further description of the corresponding embodiments: spatial discretization and temporal discretization can be performed in the following ways: spatial discretization of the flow control equations is performed using the finite volume method; temporal discretization of the flow control equations is performed using the second-order Runge-Kutta method.

[0099] As for Figure 1 In a further description of the corresponding embodiments, T can be solved in the following ways. n+1 Volume fraction and interface normal vector at time T: Solve the discretized VOF transport equation to obtain the volume flux of the control surface of the tetrahedral element; solve for the volume flux of the tetrahedral element at time T based on the volume flux of the control surface of the tetrahedral element. n+1 Volume fraction at time T; based on the tetrahedral element at time T n+1 The volume fraction at time T is obtained by solving the equation for the tetrahedral element at time T. n+1 The interface normal vector at time t.

[0100] The process described in the above embodiments is illustrated below through examples in practical applications.

[0101] Currently, the most widely used two-phase flow interface capture algorithms are the level-set method and the volume fraction of fluid (VOF) method. For compressible two-phase flows, the level-set method is mostly used to capture the interface. While this method can capture discontinuities well, its conservation properties are poor, often resulting in significant volume losses after multiple iterations. Furthermore, the level-set function needs to be reinitialized after each iteration, leading to a large computational burden. The level-set method struggles to accurately capture interfaces that break or merge during calculation. In contrast, the VOF method offers better conservation properties, lower computational cost, and is more advantageous in handling broken and merged interfaces. For interface reconstruction using the VOF method, the SLIC and PLIC methods are commonly employed. The SLIC method uses line segments or planes parallel to the coordinate plane to represent the two-phase flow interface within a cell, resulting in low accuracy. The PLIC method approximates the two-phase flow interface of each cell using inclined piecewise planes, thus achieving higher accuracy. Currently, most computational methods for compressible two-phase fluids combine the level-set method with virtual fluid methods. There is currently no solution for compressible two-phase flow that combines the PLIC-VOF method with the virtual fluid method.

[0102] To improve volume conservation, reduce volume loss, and enhance the ability to capture broken and merged interfaces in the solution process of compressible two-phase flow, this embodiment provides a compressible two-phase flow algorithm based on the PLIC-VOF method to obtain the flow field parameters of the compressible two-phase flow field. This embodiment uses tetrahedral elements and employs the piecewise planar approximation method (PLIC) to reconstruct the two-phase flow interface. A single, non-split Euler geometric algorithm is used to solve for the VOF volume flux. The flow control equations (Euler equations) are spatially discretized using the finite volume method, the control surface flux is solved using the AUSM+-UP method, and the time discretization uses the second-order Runge-Kutta method. The interface boundary is handled using the Real Virtual Flow Method (RGFM), and then the compressible flow field solver and the VOF solver are combined to establish a compressible two-phase flow algorithm. The specific implementation process is as follows:

[0103] Step 1: Select the Euler equation as the flow control equation;

[0104] Step 2: Spatial discretization of the flow control equations is performed using the finite volume method, and the flow field is initialized;

[0105] Step 3: Time discretization is performed using the second-order Runge-Kutta method;

[0106] Step 4: Solve for the flux on the non-interface element control surface using the AUSM+-UP method;

[0107] Step 5: Discretize the VOF transport equations;

[0108] Step 6: Interface Reconstruction;

[0109] The interface reconstruction process is as follows: the flow field is initialized with volume fractions, the volume fraction of the primary phase fluid is 1, and the volume fraction of the secondary phase fluid is 0; the interface normal vector is represented by the volume fraction gradient, and the normal vector is solved using the moving particle semi-implicit method (MPS); the interface mesh is divided into 3 types, and the coordinates of the intersection points between the interface and the mesh cells are solved to determine the position of the interface; the volume flux flowing through each cell is solved by the geometric cutting method, and the volume flux is subtracted from the volume of the primary phase fluid at time n, and then divided by the cell volume to obtain the cell volume fraction at time n+1.

[0110] Step 7: Perform interface boundary processing using the Real Virtual Fluid Method (RGFM), then solve for the fluid flux of the interface element, and then update the global flow field variables to obtain the flow field information at time n+1.

[0111] Step 8: Update the flow field properties. Update the flow field of each element by obtaining the volume fraction at time n+1. If the volume fraction of the element and the surrounding elements are both greater than 0.5, the fluid property is considered to be a primary phase fluid. If the volume fraction of the element and the volume fraction of the surrounding elements are both less than 0.5, the fluid property is considered to be a secondary phase fluid. The other elements retain the original fluid properties.

[0112] Specifically, the flow control equations are explained as follows:

[0113] The flow control equation is the Euler equation, whose integral form is shown in equation (1), and it is spatially discretized using the finite volume method.

[0114]

[0115] In equation (1), V is the volume of the tetrahedral element (i.e., the control volume). It is the outer boundary of the tetrahedral unit. Let dV represent the partial derivative over time, dA represent the differential of volume, and dA represent the differential of area. The definitions of the conserved variables U and the inviscid flux F are as follows:

[0116]

[0117] In equation (2), ρ, p, and E represent the fluid density, pressure, and total specific internal energy, respectively; u, v, and w are the velocity components in the X, Y, and Z directions, respectively; and n x n y and n zIt is the component of the normal n of the control surface in the X, Y, and Z directions. The normal velocity is defined by equation (3), and the relationship between the total specific internal energy E and the specific internal energy e is shown in equation (4). The X, Y, and Z directions are the three coordinate axes of the spatial rectangular coordinate system.

[0118] u n =un x +vn y +wn z (3)

[0119]

[0120] The Stiffen gas law is adopted, as shown in equation (5). Where P... c It is an extended pressure constant, and γ is the specific heat ratio.

[0121]

[0122] Specifically, the spatial discretization process is as follows:

[0123] Using the finite volume method based on the lattice center scheme, all state variables are stored at the centroid of the element. The computational domain (i.e., the target flow field mentioned above) is divided into several non-overlapping tetrahedral elements, and integral conservation is achieved within each tetrahedral element. Since the volume of each tetrahedral element does not change with time, and i represents the index of the tetrahedral element, equation (1) can be written as equation (6):

[0124]

[0125] Integrating the inviscid flux over the unit control surface, equation (6) can be written as equation (7):

[0126]

[0127] Where R i The residual is defined as shown in equation (8):

[0128]

[0129] A ij It is the area of ​​the common control surface between two adjacent tetrahedral elements i and j. The flux through the surface can be replaced by the flux at the center of the control surface. Therefore, the flux on the control surface can be approximated by equation (9):

[0130]

[0131] F ij This represents the inviscid flux on the common surface of tetrahedral element i and tetrahedral element j.

[0132] Specifically, the second-order Runge-Kutta method for time discretization of the flow control equations is explained below:

[0133] Discretizing equation (1) by time derivative yields equation (10):

[0134]

[0135] In the formula, V is the volume of the tetrahedral element. U is the average value of the state variables of tetrahedral element i. i It is the state variable value at the centroid of the tetrahedral element. Equation (10) can be written as equation (11) and equation (12):

[0136]

[0137]

[0138] In equation (12), the superscript n or n+1 of each letter represents time n or time n+1, and Δt represents the time step, that is, the time difference between time n and time n+1 (the iteration period mentioned above).

[0139] Considering two-step time discretization of equation (12), we can obtain equations (13) and (14):

[0140]

[0141]

[0142] L h A function representing the state variable U, with U as the independent variable, can be expressed as:

[0143] Specifically, the solution for the control surface flux is explained below:

[0144] The AUSM+-up method is used to solve for flux on the control surface, and second-order accuracy is constructed on the control surface.

[0145] The AUSM+-UP format for flux calculation can be written as equations (15) to (17), where M ij It is the Mach number at the interface between the two units, defined by equation (18), a ij It is the speed of sound at the interface between the two units.

[0146]

[0147]

[0148]

[0149]

[0150] In the above formula The flow field variables shown in equation (16) on the left side of the interface between the two units are represented. The flow field variables shown in equation (16) on the right side of the interface between the two units are represented by p; p represents pressure, ρ L ρ represents the density on the left side of the interface between the two elements. R M represents the density on the right side of the interface between the two units; L M represents the Mach number on the left side of the interface between the two units. R This represents the Mach number on the right side of the interface between the two units; and The meaning is shown in equation (23). The meaning is shown in equation (20), K p f a σ represents the first, second, and third coefficients used to correct the dissipation term.

[0151] Pressure flux P ij The calculation formula is as follows:

[0152]

[0153] and Let K be a function of M. u U represents the correction factor. R The velocity u represents the velocity on the right side of the interface between the two units. L This indicates the velocity on the left side of the interface between the two units.

[0154] The terms in equations (18) and (19) are defined as follows:

[0155]

[0156] In the above formula, q L q represents the sum of the squares of the velocities in the three directions on the left side of the interface between the two units. R This represents the sum of the squares of the velocities in the three directions on the right side of the interface between the two units.

[0157] q 2 =u 2 +v 2 +w 2 ; (twenty one)

[0158]

[0159] In the above formula, This represents the square of the incoming Mach number.

[0160]

[0161]

[0162] Please see Figure 2 , Figure 2 This is a schematic diagram illustrating a high-order format construction provided in an embodiment of this application. Figure 2 In this context, P0, P1, P2, and P3 represent the numbers of the tetrahedral elements, and A, B, and C represent the points within the tetrahedral elements. In tetrahedral element P0, Ω1 represents the primary phase fluid, and Ω2 represents the secondary phase fluid. The reconstructed value of the variable at any point (x, y, z) can be expressed as equation (25):

[0163]

[0164] In the above formula, (x0, y0, z0) represent the centroid coordinates of the tetrahedral element P0. Let Δr represent the gradient of the variable, and let Δr represent the vector between points.

[0165] Specifically, the discretization of the transport equations by VOF is explained as follows:

[0166] A volume fraction scalar field function f(x,t) is defined for each fluid, as shown in the following equation:

[0167]

[0168] The volume fraction F of the main phase fluid in each cell is calculated as shown in the following formula.

[0169]

[0170] In equation (27), V c The transport equation for the VOF scalar function f(x,t) representing the volume of the unit is shown in equation (28).

[0171]

[0172] In the above formula, This represents the Nabla operator.

[0173] Discretizing equation (28) yields:

[0174]

[0175] In the formula A k It is the area of ​​the k-th face of the unit, n k V is the outward normal direction of the k-th face of the element. nk V is the normal velocity of the k-th face of the element. c Let be the element volume. Equation (29) transforms the problem into solving for the net volume flux of the VOF scalar function through each control surface of the element.

[0176] Specifically, the interface reconstruction is explained as follows:

[0177] VOF initialization: Assign values ​​to the volume fraction of all elements in the flow field, setting the volume fraction of the primary phase fluid to 1 and the volume fraction of the secondary phase fluid to 0.

[0178] (1) Solution of interface normal: The gradient of the volume fraction is used to replace the normal, and the moving particle semi-implicit method (MPS) is used for solution, such as Figure 3 As shown, Figure 3 This is a schematic diagram of solving the VOF interface normal provided in an embodiment of this application. F0 represents the volume fraction of the element whose normal is to be solved, 1, 2, and 3 represent the element vertices, and F1, F2, and F3 represent the volume fractions of the element vertices.

[0179] As shown in equation (30), and it is defined that the direction from inside the main phase fluid to outside the main phase fluid is positive, the solution formula of the MPS method is shown in equation (31).

[0180]

[0181]

[0182] In the above formula, (x p y p , z p () represents the coordinates of each vertex of the cell. This represents the average volume fraction of all elements that share a vertex with a given element.

[0183] (2) Interface location determination: Each unit vertex is numbered, denoted by A, B, C, and D, ensuring that vertex A is within the main phase fluid. The units can be divided into three types, such as... Figure 4 As shown, Figure 4 This is a schematic diagram illustrating the classification of interface units provided in an embodiment of this application. Figure 4 In the diagram, (a) represents the first type of unit, (b) represents the second type of unit, and (c) represents the third type of unit. A, B, C, D, E, F, G, H, I, J, K, and L are points on the tetrahedral units. The classification method is as follows: Using the given normal vector n, draw a plane through vertex B, as shown below. Figure 4 As shown in (a), the plane intersects AC and AD at points F and E, respectively. The volume ratio of tetrahedron ABEF to ABCD can be written as equation (32).

[0184]

[0185] V ABEF V represents the volume of tetrahedron ABEF. ABCD Let S represent the volume of tetrahedron ABCD. AEFLet S represent the area of ​​triangle AEF. ACD Let d represent the area of ​​triangle ACD. Assume a plane passes through point A, and the normal vector of the plane is the normal to the two-phase flow interface within the element. B d C d D Let be the distances from points B, C, and D to the plane.

[0186] Similarly, a plane is drawn through vertex C using a given normal vector n. The plane intersects DA and DB at points L and K, respectively, as shown. Figure 4 As shown in (c), the volume ratio of tetrahedron DCKL to ABCD can be written as equation (33).

[0187]

[0188] V DCKL V represents the volume of the tetrahedron DCKL. ABCD Let S represent the volume of tetrahedron ABCD. DKL Let S represent the area of ​​triangle DKL. ABD Let f represent the area of ​​triangle ABD. If the fluid volume fraction F ≤ f B If F ≥ 1 - f, then it is a first-class unit. C If d , then it is a third-class unit; otherwise, it is a second-class unit. However, some special cases may arise during the calculation. If d B =0, then f B =0, points E and F collapse to vertex A. The following formula also applies to these special cases. The only thing to note is that, to avoid the denominator being 0, in actual programming, d needs to be explicitly set. C =d B =d A The case where f = 0 is classified as the third category, and let f C =1, and d D =d C =d B The case is classified as the second category, and let f B =1.

[0189] After classifying the elements, the coordinates of the intersection points between the interface and the tetrahedral elements are solved for each element type. For the first and third types of elements, the coordinates of points G, H, and I are solved, and for the second type of elements, the coordinates of points G, H, I, and J are solved, thus determining the position of the interface.

[0190] (3) Solving for the volume flux of a cell: Knowing the volume fraction at time n, to obtain the volume fraction at time n+1, it is necessary to solve for the volume flux at time n. The method for solving the volume flux is described using a first-type mesh as an example. Figure 5 As shown, Figure 5This diagram illustrates an interface volume flux calculation method provided in an embodiment of this application. The volume flux calculation for other mesh surfaces is similar.

[0191] Suppose a plane μ parallel to surface ABD intersects the element edges at points P1, P2, and P3, and the distance between plane μ and surface ABD is V. n *Δt,V n To solve for the normal velocity of the plane, Δt is the time step; only V is calculated. n In the case of the out-of-plane normal direction, the principal phase fluid intercepted by the plane is the volumetric flux flowing out of this plane. Let h H Let h be the distance from point H to surface ABD. H <V n *Δt, then the outflow flux is the total flux of the main phase fluid V. AGHI If h H >V n Given *Δt, the flux at the outflow surface ABD is: Figure 5 The volume of the shaded area is calculated. The volume fraction flux of the remaining faces of the element is calculated using the same method, and then integrated to obtain the volume flux flowing out of the entire element. Then, the volume flux flowing out of the element is subtracted from the volume flux of the main phase fluid at time n to obtain the volume of the main phase fluid at time n+1. Dividing this by the element volume gives the volume fraction of the element at time n+1.

[0192] Specifically, the construction process of interface boundary conditions is as follows: In the calculation of compressible two-phase flow, due to the significant difference in physical properties between the media on both sides of the interface, discontinuities occur. Directly calculating the convective flux of the interface elements can cause non-physical oscillations or even computational divergence. To accurately solve the discontinuity problem at the interface, the interface elements need to be processed. This patent employs a Real Virtual Fluid Method (RGFM) with good strong discontinuity solution for interface boundary processing.

[0193] The boundary conditions on both sides of the interface are shown in the diagram. Figure 6 and Figure 7 As shown, Figure 6 This is a schematic diagram illustrating the establishment of boundary conditions at a two-phase flow interface, as provided in an embodiment of this application. Figure 7 This is a schematic diagram of a virtual fluid structure provided in an embodiment of this application. Figure 6 In the diagram, A represents fluid A, A* represents a virtual fluid of fluid A, and U... A S represents the state variable of fluid A. A V represents the entropy of fluid A. A P represents the velocity of fluid A. A This represents the pressure of fluid A. B represents fluid B, B* represents a virtual fluid of fluid B, and U... B S represents the state variable of fluid B. B V represents the entropy of fluid B.B P represents the velocity of fluid B. B This indicates the pressure of fluid B. Figure 7 China e L and e R These represent the names of the left and right units of the interface, U. L and U R This represents the state variables of the left and right cells of the interface. and This represents the intermediate state variables obtained by solving the left and right states of the unit Riemann problem.

[0194] Define three physical quantities: density ρ, velocity V, and pressure P. To determine the density, velocity, and pressure of the fluid in region A at time n+1, we need to assign values ​​to the virtual elements within region A. In the one-dimensional case at the two-phase interface, entropy is discontinuous due to physical reasons, but pressure and velocity are continuous. Therefore, the pressure and velocity of the virtual elements in region A can be directly assigned the pressure and velocity of the fluid in region B. Because entropy is discontinuous, its value in the virtual element can be determined by extrapolation, as shown in the following formula:

[0195]

[0196] In the above formula, S represents the entropy of the fluid.

[0197] For two-dimensional and three-dimensional cases, tangential velocity is added; this explanation will focus on two-dimensional cases. Interpolation needs to be performed along the interface normal, therefore normal velocity and pressure are continuous, while tangential velocity and density are discontinuous. The handling of normal velocity, pressure, and entropy can be referenced from the one-dimensional case; other variables require separate solutions.

[0198] Assume the state variables U of the units on both sides of the interface L，R As shown in equation (35).

[0199] U L，R =[p L，R V L，R , ρ L，R ]; (35)

[0200] In equation (35), the velocity of the interface consists of normal velocity and tangential velocity components, as shown in equation (36):

[0201]

[0202] In the above formula, The vector represents the normal velocity, and n represents the normal direction vector. τ represents the tangential velocity, and τ is the tangential direction vector.

[0203] Project the state variables of the units on both sides of the interface onto the interface normal direction, as shown in Equation (37). Then solve the Riemann problem to reconstruct new interface state variables. These variables are recombined from the Riemann problem solution and the intermediate state of the tangential velocity, as shown in Equation (38).

[0204]

[0205]

[0206] In equation (38), the subscript I represents the intermediate state variable obtained from the Riemann problem, and then the state variables of the elements on both sides of the interface are updated using the Riemann solution. The information of the virtual fluid element can be obtained by extrapolation through the updated state variables of the element. After constructing the virtual fluid element, the fluid flux of the interface element is solved.

[0207] Specifically, the process of updating the flow field properties is as follows:

[0208] All computational units are divided into two regions, Ω1 and Ω2, with each unit centroid corresponding to a fluid medium state, defined by equation (39):

[0209]

[0210] The volume fraction can be reconstructed according to equation (40):

[0211]

[0212] In equation (40), (i′, j′) are adjacent units, α and β are 1 or 2 and are not equal. The units near the interface with volume fractions not equal to 0 and 1 are traversed. If the volume fraction of the unit and the surrounding units are both greater than 0.5, the fluid property is considered to be Ω1. If the volume fraction of the unit and the volume fraction of the surrounding units are both less than 0.5, the fluid property is considered to be Ω2. The remaining units retain their original fluid properties.

[0213] Please see Figures 8 to 14 , Figure 8 This is a schematic diagram illustrating the interface capture effect after spherical deformation recovery, provided in an embodiment of this application. Figure 9 This is a schematic diagram illustrating the interface capture effect of spherical shear deformation provided in an embodiment of this application. Figure 10 This is a comparison chart of numerical results and exact solutions for a water vapor shock tube in the density dimension, provided in an embodiment of this application. Figure 11 This is a comparison chart of numerical results and exact solutions for a water-gas shock tube in the pressure dimension, provided in an embodiment of this application. Figure 12 This is a comparison chart of numerical results and exact solutions for a water-air shock tube in the velocity dimension, provided in an embodiment of this application. Figure 13This is an isosurface diagram of the interface between a shock wave and a helium bubble, provided in an embodiment of this application. Figure 14 This is a symmetrical cross-sectional density cloud map of the interaction between a shock wave and a helium bubble, provided as an embodiment of this application. Figure 10 The horizontal axis represents the dimensionless length (total length is 1), and the vertical axis represents the density; Exact-density represents the exact solution of the density, and density represents the numerical solution (i.e., the numerical solution of the density calculated by the method in this embodiment). Figure 11 The horizontal axis represents dimensionless length (total length is 1), and the vertical axis represents pressure. Exact-p represents the exact solution of pressure, and p represents the numerical solution of pressure. Figure 12 The horizontal axis represents the dimensionless length (total length is 1), the vertical axis represents the velocity, Exact-u represents the exact solution of the velocity, and u represents the numerical solution of the velocity. Figure 14 Density represents density. Figure 11 and Figure 12 In this context, E represents scientific notation.

[0214] This embodiment combines the PLIC-VOF method with the Real Virtual Flow Method (RGFM) to solve compressible two-phase flows and extends it to the calculation of three-dimensional flow fields based on tetrahedral elements, forming a new algorithm for solving compressible two-phase flows. Compared with traditional level-set-based algorithms for compressible two-phase flows, this algorithm simplifies the calculation process, reduces the number of iterations, improves the ability to handle interface fusion and fragmentation, and enhances the conservation properties in compressible two-phase flow calculations.

[0215] This application also provides a flow field parameter determination system for a compressible two-phase flow, which may include:

[0216] The flow field determination module is used to determine the target flow field when a target object moves in a compressible two-phase fluid;

[0217] An initialization module is used to divide the target flow field into multiple tetrahedral elements and initialize the target flow field at T. n Flow field information and volume fraction at any given time;

[0218] The discrete processing module is used to determine the flow control equations of the target flow field and to perform spatial and temporal discretization operations on the flow control equations.

[0219] The first flux determination module is used to solve the flow control equations after the spatial discretization operation and the time discretization operation, and obtain the flux determination at time T. n The flux on the control surface of the non-interface unit at time T; wherein, the non-interface unit is not in the target flow field at time T nTetrahedral elements at the interface between two phases at a given time;

[0220] The second flux determination module is used to process the interface elements using a realistic virtual fluid method and solve for the flux at T. n The flux on the control surface of the interface unit at time T; wherein, the interface unit is located in the target flow field at time T n Tetrahedral elements at the interface between two phases at a given time;

[0221] The flow field information update module is used to update the flow field information based on the flow field information at T. n The flux generated on the control surface of the non-interface unit and the interface unit at time T generates the target flow field. n+1 Flow field information at any given moment;

[0222] The interface update module is used to solve the discretized VOF transport equation to obtain the interface update of all the tetrahedral elements at T. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1 The interface between the two phases at a given moment;

[0223] The iteration judgment module is used to determine whether the iteration termination condition has been met; if so, it outputs the T value. n+1 The flow field information at time T and the T n+1 The two-phase flow interface at time n; if not, increment the value of n by 1 and proceed to the processing flow of the discrete processing module.

[0224] In this embodiment, after determining the target flow field of the target object moving in a compressible two-phase fluid, the target flow field is divided into multiple tetrahedral elements and initialized. After initializing the target flow field, this embodiment determines the flow field information and the two-phase interface at each time step through iterative calculation. During the iteration process, this embodiment solves the flow control equations after spatial and temporal discretization operations to obtain the flow field information at time step T. n The flux on the control surface of the non-interface element at time T; this embodiment also processes the interface element and solves for the flux at time T using a real virtual fluid method. n The flux on the control surface of the interface unit at time T is used to obtain the target flow field at time T. n+1 In this embodiment, the flow field information at time T is obtained by solving the discretized VOF transport equations. n+1 The volume fraction and interface normal vector at time T are used to determine the target flow field at time T. n+1The interface between the two phases at a given time. The iterative process described above combines the VOF method with the real-virtual flow method to solve for compressible two-phase flows. Compared to compressible two-phase flow algorithms based on the Level-set method in related technologies, this embodiment simplifies the calculation process and improves the ability to handle interface fusion and interface fragmentation. Therefore, this embodiment can reduce the number of iterations and computational load for determining the flow field parameters of compressible two-phase flows, and improve the conservation properties in the calculation of compressible two-phase flows.

[0225] Furthermore, the process of the discretization module performing spatial and temporal discretization operations on the flow control equations includes: performing spatial discretization operations on the flow control equations using the finite volume method; and performing temporal discretization operations on the flow control equations using the second-order Runge-Kutta method.

[0226] Furthermore, the first flux determination module solves the flow control equations obtained after the spatial and temporal discretization operations to obtain the flux at time T. n The flux process on the control surface of the non-interface unit at time T includes: solving the flow control equations after the spatial and temporal discretization operations using the AUSM+-UP method to obtain the flux at time T. n The flux on the control surface of the non-interface unit at that moment.

[0227] Furthermore, the second flux determination module processes the interface elements using a realistic virtual fluid method and solves for the flux at T. n The process of determining the flux on the control surface of the interface unit at any given time includes: performing interface boundary processing on the interface unit using a real virtual fluid method, and using the interface boundary processing results to solve for the flux on the control surface of the interface unit.

[0228] Furthermore, the interface update module solves the discretized VOF transport equation to obtain the values ​​of all the tetrahedral elements at T. n+1 The process of determining the volume fraction and interface normal vector at time T includes: solving the discretized VOF transport equation to obtain the volume flux of the control surface of the tetrahedral element; and solving for the volume flux of the tetrahedral element at time T based on the volume flux of the control surface of the tetrahedral element. n+1 Volume fraction at time T; based on the tetrahedral element at time T n+1 The volume fraction at time T is obtained by solving the equation for the tetrahedral element at time T. n+1 The interface normal vector at time t.

[0229] Furthermore, the process by which the iterative judgment module determines whether the iteration termination condition has been met includes: determining T n Is the time the preset time? (T) n+1 With T nThe difference is the iteration period; if it is, then the iteration termination condition is determined to have been met; if not, then the iteration termination condition is determined not to have been met.

[0230] Furthermore, the process by which the flow field determination module determines the target flow field when the target object moves in a compressible two-phase fluid includes: determining the target flow field when the propeller moves in a compressible two-phase fluid; wherein the compressible two-phase fluid is water and air, respectively;

[0231] Correspondingly, it also includes:

[0232] Adjustment module, used to output the T n+1 The flow field information at time T and the T n+1 After the two-phase flow interface at time T, according to the above... n+1 The flow field information at time T and the T n+1 The mechanical damage level of the propeller is calculated at the two-phase flow interface at a given time; the blade shape of the propeller is adjusted according to the mechanical damage level.

[0233] Since the embodiments of the system part correspond to the embodiments of the method part, please refer to the description of the embodiments of the method part for the embodiments of the system part, and they will not be repeated here.

[0234] This application also provides a storage medium on which a computer program is stored, which, when executed, can perform the steps provided in the above embodiments. The storage medium may include various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0235] This application also provides an electronic device that may include a memory and a processor. The memory stores a computer program, and when the processor calls the computer program in the memory, it can implement the steps provided in the above embodiments. Of course, the electronic device may also include various network interfaces, power supplies, and other components.

[0236] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to in the method section. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

[0237] It should also be noted that, in this specification, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A method for determining the flow field parameters of a compressible two-phase flow, characterized in that, include: Step 1: Determine the target flow field when the target object moves in a compressible two-phase fluid; Step 2: Divide the target flow field into multiple tetrahedral elements, and initialize the target flow field at T. n Flow field information and volume fraction at any given time; Step 3: Determine the flow control equations for the target flow field, and perform spatial and temporal discretization operations on the flow control equations; Step 4: Solve the flow control equations obtained after the spatial and temporal discretization operations using the AUSM+-UP method to obtain the flow control equations at time T. n The flux on the control surface of the non-interface unit at time T; wherein, the non-interface unit is not in the target flow field at time T n Tetrahedral elements at the interface between two phases at a given time; Step 5: Perform interface boundary processing on the interface unit using a realistic virtual fluid method, and use the interface boundary processing results to solve for the flux on the control surface of the interface unit; wherein, the interface unit is located in the target flow field at T n Tetrahedral elements at the interface between two phases at a given time; Step 6: Based on T n The flux generated on the control surface of the non-interface unit and the interface unit at time T generates the target flow field. n+1 Flow field information at any given moment; Step 7: Solve the discretized VOF transport equations to obtain the volume flux of the control surface of the tetrahedral element; solve for the volume flux of the tetrahedral element at T based on the volume flux of the control surface of the tetrahedral element. n+1 Volume fraction at time T; based on the tetrahedral element at time T n+1 The volume fraction at time T is obtained by solving the equation for the tetrahedral element at time T. n+1 The interface normal vector at time T; the target flow field at time T is determined based on the volume fraction and the interface normal vector. n+1 The interface between the two phases at a given moment; Step 8: Determine if the iteration termination condition has been met; if so, output the given T. n+1 The flow field information at time T and the T n+1 The two-phase flow interface at time n; if not, increment the value of n by 1 and proceed to step 4.

2. The method for determining the flow field parameters of a compressible two-phase flow according to claim 1, characterized in that, The flow control equations are subjected to spatial and temporal discretization operations, including: The flow control equations are spatially discretized using the finite volume method. The flow control equations are discretized in time using the second-order Runge-Kutta method.

3. The method for determining the flow field parameters of a compressible two-phase flow according to claim 1, characterized in that, The determination of whether the iteration termination condition has been met includes: Determine T n Is the time the preset time? (T) n+1 With T n The difference is the iteration period; If so, then the iteration termination condition is determined to have been met; If not, then the iteration termination condition has not been met.

4. The method for determining the flow field parameters of a compressible two-phase flow according to claim 1, characterized in that, Determining the target flow field when the target object moves in a compressible two-phase fluid includes: Determine the target flow field when a propeller moves in a compressible two-phase fluid; wherein the compressible two-phase fluid is water and air. Accordingly, in the output of T n+1 The flow field information at time T and the T n+1 Following the two-phase flow interface at a given time, it also includes: According to the T n+1 The flow field information at time T and the T n+1 The mechanical damage level of the propeller is calculated at the two-phase flow interface at a given time. The propeller blade shape is adjusted according to the level of mechanical damage.

5. A system for determining the flow field parameters of a compressible two-phase flow, characterized in that, include: The flow field determination module is used to determine the target flow field when a target object moves in a compressible two-phase fluid; An initialization module is used to divide the target flow field into multiple tetrahedral elements and initialize the target flow field at T. n Flow field information and volume fraction at any given time; The discrete processing module is used to determine the flow control equations of the target flow field and to perform spatial and temporal discretization operations on the flow control equations. The first flux determination module is used to solve the flow control equations after the spatial and temporal discretization operations using the AUSM+-UP method, to obtain the flux determination at time T. n The flux on the control surface of the non-interface unit at time T; wherein, the non-interface unit is not in the target flow field at time T n Tetrahedral elements at the interface between two phases at a given time; The second flux determination module is used to perform interface boundary processing on the interface unit using a realistic virtual fluid method, and to solve for the flux on the control surface of the interface unit using the interface boundary processing result; wherein, the interface unit is located in the target flow field at T n Tetrahedral elements at the interface between two phases at a given time; The flow field information update module is used to update the flow field information based on the flow field information at T. n The flux generated on the control surface of the non-interface unit and the interface unit at time T generates the target flow field. n+1 Flow field information at any given moment; The interface update module is used to solve the discretized VOF transport equations to obtain the volume flux of the control surface of the tetrahedral element; it is also used to solve the T-interface update module based on the volume flux of the control surface of the tetrahedral element. n+1 The volume fraction at time T; also used to determine the volume fraction of the tetrahedral unit at time T n+1 The volume fraction at time T is obtained by solving the equation for the tetrahedral element at time T. n+1 The interface normal vector at time T; also used to determine the target flow field at time T based on the volume fraction and the interface normal vector. n+1 The interface between the two phases at a given moment; The iteration judgment module is used to determine whether the iteration termination condition has been met; if so, it outputs the T value. n+1 The flow field information at time T and the T n+1 The two-phase flow interface at time n; if not, increment the value of n by 1 and proceed to the processing flow of the discrete processing module.

6. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the flow field parameter determination method for compressible two-phase flow as described in any one of claims 1 to 4.

7. A storage medium, characterized in that, The storage medium stores computer-executable instructions, which, when loaded and executed by a processor, implement the steps of the flow field parameter determination method for compressible two-phase flow as described in any one of claims 1 to 4.

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