A method for solving mixer motion coupling based on ACMI and AMI

Abstract

The application discloses a mixer motion coupling solving method based on ACMI and AMI, belongs to the technical field of mixer motion simulation and emulation, and comprises the following steps: according to existing mixer equipment drawings, digital modeling of the mixer equipment is carried out by using three-dimensional modeling software; AMI algorithm is used to realize simulation of the rotating motion of a local area of a stirring tool head; ACMI algorithm is used to realize simulation of long-distance translational motion of the mixer equipment; grid generation is calculated; the grid of a motion area and the grid of a static area are respectively generated; motion control is realized for different cellZone in the model; initial conditions and boundary conditions of the model are set, and running solving is carried out to obtain the spatial distribution and concentration of the solidifying agent (uniformity of stirring). The ACMI sliding mechanism makes the grid nodes only have rigid body displacement in the motion, and do not have deformation. The grid quality does not decrease with the increase of drilling depth, and the stability of the whole process calculation is ensured.

Description

Technical Field

[0001] This invention relates to the field of mixer motion simulation technology, and in particular to a mixer motion coupling solution method based on ACMI and AMI. Background Technology

[0002] With the advancement of my country's "Maritime Power" strategy and the rapid development of the coastal economic belt, the construction of large-scale marine and coastal engineering projects such as cross-sea bridges, subsea tunnels, offshore wind power, artificial islands and reefs, and port terminals is increasing. Most of these projects are located on soft soil foundations, with extremely complex geological conditions. Coastal soft soil generally exhibits the physical and mechanical characteristics of "three highs and one low": High water content: large void ratio, with natural water content often exceeding the liquid limit. High compressibility: easily undergoing large settlement deformation under external loads. High sensitivity: rapid decrease in strength after structural disturbance. Low bearing capacity: extremely low shear strength, unable to directly support heavy structures. Furthermore, the coastal soft soil environment is also affected by multiple dynamic and environmental factors such as tidal cycles, wave impact, saltwater chemical erosion, and frequent fluctuations in groundwater levels. In particular, the soil often contains high levels of organic matter, which not only reduces the engineering properties of the soil but also hinders the hydration reaction of cement and other hardening agents, exponentially increasing the difficulty of foundation treatment.

[0003] Deep mixing is currently the mainstream technology for solving deep soft soil foundation problems. Its basic principle is to use a specially designed deep mixer to inject a solidifying agent into the soil slurry. Through the forced shearing and mixing action of the mixing blades, the solidifying agent undergoes a physicochemical reaction with the in-situ soft soil, forming a solidified body with high strength and low permeability, thereby improving the bearing capacity of the foundation. The mixer mainly consists of a mixing head, a solidifying agent spray pipe, and corresponding support structures, as shown in the diagram. Figure 1 As shown. However, in practical engineering, the application of deep mixing technology faces serious quality control challenges. For example, due to the invisibility of underground construction, the distribution of the curing agent in the soil often exhibits a high degree of randomness. Common phenomena such as "half-grown," "broken piles," or insufficient core strength are mostly attributed to uneven mixing. However, the complexity of the mixing structure, physical process, and site conditions makes it difficult to effectively evaluate and optimize the parameters of the mixing process through physical model tests. Therefore, numerical simulation has become an indispensable research method.

[0004] Computational Fluid Dynamics (CFD) is a common method for numerical simulation of deep mixing operations. Generally, soft soil slurry and solidifying agents typically have high water content, which can be considered equivalent to two fluids of different viscosities. CFD can then be used to simulate the mixing process of these two fluids during the mixing equipment operation. However, traditional commercial software or algorithms have the following limitations in handling complex mixing equipment operations: The motion characteristics of a deep mixer are a superposition of "large macroscopic displacement (vertical feed)" and "rapid local rotation (blade rotation)". Traditional dynamic mesh methods based on stretching or local reconstruction often result in severe mesh stretching or compression when handling vertical displacements of several meters or even tens of meters, easily leading to negative volume errors and computational divergence. Even though some commercial software can handle large-scale displacement processes based on its proprietary software technology, such as Flow3D's FAVOR technology, they typically require extremely large mesh sizes to finely capture the complex agitator head structure. Figure 2 The paper presents the agitator head structure captured by Flow3D under relatively low mesh resolution conditions. It can be found that the capture of the rotating agitator head and the hardener nozzle is severely distorted, thus affecting the simulation accuracy. Furthermore, even under such low mesh resolution conditions, simulating a complete up-and-down motion of the agitator structure requires at least 30 days of computation time, resulting in low computational efficiency. Existing software often simplifies mud as a Newtonian fluid or a simple power-law fluid. In reality, soft soil mud containing clay particles exhibits significant yield stress and shear thinning characteristics, classifying it as a typical viscoplastic fluid. Ignoring yield stress can lead to misjudgments of dead zones and stirring torque. Summary of the Invention

[0005] This invention provides a method for solving the motion coupling of a mixer based on ACMI and AMI, and develops a numerical solution method based on OpenFOAM that can be used to simulate the coupling process of complex motion of the stirring head and multiphase jet.

[0006] According to one aspect of this disclosure, a method for solving the motion coupling of a mixer based on ACMI and AMI is provided, the method comprising: Based on the existing drawings of the mixing equipment, a digital model of the mixing equipment is created using 3D modeling software. The AMI algorithm is used to simulate the rotational motion of a local area of ​​the agitator head; The simulation of long-distance translational motion of a stirring device is achieved using the ACMI algorithm, including: determining the complete computational domain, which consists of two independent regions: a stationary region and an intermediate moving region. The stationary region is hollow. Computational mesh generation: Generate meshes for the moving region and the stationary region respectively; Motion control: The multiSolidBodyMotionSolver in OpenFOAM is used to solve the object motion problem and achieve motion control for different grid zones in the model. The initial and boundary conditions of the model are set, and the model is run to solve for the spatial distribution and concentration of the curing agent. The initial conditions include the volume fraction of the concentration field at the initial moment, and the boundary conditions include: the inlet boundary, the outlet boundary, and the solid boundary of the stirring device.

[0007] In one possible implementation, the mixing equipment is digitally modeled using 3D modeling software based on existing mixing equipment drawings, including: During the modeling process, the mixing equipment was divided into three parts according to its motion: the left and right blades, the middle part, and the fixed support and nozzle pipeline. During the segmentation modeling process, it is necessary to ensure that the left and right sides of the swivel head and its supporting structure are completely fitted, that is, the planes of the two sides of the swivel head and its supporting structure have the same center position, radius and tilt angle. Ensure that all faces on the left and right cutter head structures in the model can form a complete closed solid, and export the solids of the left and right cutter heads in the format of STL file, named rotate_left and rotate_right respectively; The entire pipeline nozzle and support structure also need to be exported as an STL file. The surface at the pipeline nozzle should be named INLET so that the surface at the pipeline nozzle can be identified as the inflow boundary when meshing later. The agitator head involves rotational and translational motion, while the fixed bracket and nozzle piping involve translational motion.

[0008] In one possible implementation, the mixing equipment is digitally modeled using 3D modeling software based on existing mixing equipment drawings, and the method further includes: First, export the parts other than the nozzle surface in ASCII encoding and name them "other". Then export the individual nozzle surfaces in ASCII encoding format and name them INLET; Open both STL files using Notepad, an ASCII text editor, and copy all the contents of the INLET file to the 'other' file and save it.

[0009] In one possible implementation, the mixing equipment is digitally modeled using 3D modeling software based on existing mixing equipment drawings, and the method further includes: In order to construct the rotating and non-rotating regions during the meshing process, a pair of cylindrical AMI sliding mesh boundaries need to be added near the swivel head during modeling. The range of these sliding mesh boundaries is slightly larger than the range of the swivel head, so that the swivel head can be completely included within the sliding boundary. The two AMI boundaries also need to form a closed solid and be exported as STL files, named AMI_left and AMI_right respectively.

[0010] In one possible implementation, computational grid generation includes: When generating the mesh for the moving region, the geometric dimensions of the mixing equipment can be used to determine the mesh area to completely include the mixing equipment in the xy direction. This can be achieved by extending the outermost edge of the vertical projection dimension of the mixing equipment by 0.1D (where D is the diameter of the generated AMI boundary entity). In the z direction, the top of the mesh calculation area needs to completely include the top of the mixing equipment, and the bottom needs to match the mesh of the stationary region. Initially, the bottom of the mesh in the moving region and the bottom of the mesh in the stationary region are on the same horizontal plane.

[0011] In one possible implementation, computational grid generation also includes: The background mesh of the motion region is initially divided using the blockMesh command in OpenFOAM. The mesh can be a hexahedral mesh with a cell size of 0.05D. When dividing the mesh, the generated background mesh region is set as a cellZone and given the name C3Zone, which is used to control its motion process through different cellZones later. After the background mesh is generated, all the previously generated STL files are placed in the constant / triSurface path in the example directory, and the snappyHexMesh command in OpenFOAM is used to mesh the area near the mixing device. Before running the snappyHexMesh command, set the relevant parameters in its control dictionary file. The main operations that need to be modified are as follows: disable the command to add boundary layers; add recognition of the INLET surface in the other.stl file and name it the inlet boundary, and give the boundary type as patch; use the STL files of two AMI boundaries to divide the computational region, set the region inside the two boundary surfaces as the dynamic domain, and set cellZone for the two dynamic domains, naming them C1Zone and C2Zone. Running the snappyHexMesh command will generate the computational domain mesh for the dynamic domain; The path to the control dictionary file is system / snappyHexMeshDict.

[0012] In one possible implementation, computational grid generation also includes: For the mesh of the static region, the pointwise software is used to generate it. The static region is a hollow cube structure, and its boundary scale range can be set according to the range to be simulated. The internal boundary of the hollow part of the stationary area needs to coincide with the external boundary of the moving area, and the grid scale near the hollow area needs to be similar to the grid scale on the boundary of the moving area to ensure accuracy during data exchange. To reduce computational cost, the distribution of the grid in the static region on the xy plane is a gradual change from denser in the hollow areas to sparser at the outside. After the meshes for both the moving and stationary regions are generated, the mergeMesh command in OpenFOAM is used to merge the meshes of the moving and stationary regions into a complete computational domain.

[0013] In one possible implementation, computational grid generation also includes: Motion control includes: For C1Zone and C2Zone, their motion is decomposed into a superposition of rotational motion and linear motion; The multiMotion method in solidBodyMotionFunction is used to implement superimposed motion.

[0014] In one possible implementation, the computational mesh generation also includes: dividing the motion form into one and two, where one is linear motion and its motion speed needs to be specified; and two is rotational motion and the rotation axis, rotation origin, and rotational angular velocity need to be specified. The rotation axis is the normal vector of the center of the agitator cylinder, and the rotation origin needs to be any point on the normal vector. For C3Zone, only linear motion control is required, and its motion speed needs to be exactly the same as the linear motion speed of the rotating area.

[0015] In one possible implementation, initial and boundary conditions are set for the model, and the solution is run to obtain the spatial distribution and concentration of the curing agent, including: First, the volume fraction of the concentration field at the initial moment is set to 0, which means that the calculation area at the initial moment is all mud. For the computational domain boundary, the solid boundary of the mixing device needs to be set to the movingWallVelocity boundary to account for the flux difference caused by wall movement; The movingWallVelocity boundary is a specific boundary condition already present in OpenFOAM, which ensures that the velocity of the fluid near the moving solid surface is the same as the velocity of the solid, so as to reach the no-slip boundary. For the nozzle location, set it as the inflow boundary, specify the inflow volumetric flow rate or velocity, and set the concentration field volume fraction at the nozzle boundary to 1; after setting, run the solver of the above model to solve it, or call the mpi command to solve the model in parallel over the computational domain, including: The Bingham-Papanastasiou model was used to characterize the viscosity changes of mud or solidifying agent solutions under different strain rates. The k-ω SST model, modified by the buoyancy term, was used for turbulence closure and was used to predict boundary layer separation flow under the influence of the reverse pressure gradient. The k-ω SST model is a model that considers the influence of the density change of the mixed fluid on turbulence generation. The solid boundaries of a mixing device include the agitator head, the support structure, and the boundaries of the pipe sidewalls.

[0016] Compared with the prior art, the beneficial effects of the present invention are: To address the bottlenecks of traditional commercial software (such as Flow3D) in simulating the complex motion of "long-distance vertical feed + local high-speed rotation + multiphase jet flow," including severe mesh distortion, low computational efficiency, and poor conservation, this invention proposes an innovative solution based on the OpenFOAM open-source platform. By utilizing a dynamic mesh topology structure nested between the arbitrary coupled mesh interface method and the AMI sliding mesh method, fully coupled simulation of the complex motion process of a mixer operation is achieved. Simultaneously, considering the complex rheological properties of soft soil slurry and solidifying agent, a Bingham-Papanastasiou regularized constitutive model is introduced, taking into account the influence of strong shear forces on the viscosity of the slurry and solidifying agent, thus achieving high-fidelity reproduction of the multiphase non-Newtonian fluid mixing process.

[0017] This invention solves the fundamental problem of "mesh distortion": Compared to traditional dynamic meshes, the ACMI slip mechanism of this invention ensures that mesh nodes undergo only rigid body displacement during movement, without deformation. Mesh quality does not decrease with increasing drilling depth, guaranteeing the stability of the entire calculation process.

[0018] Significantly improved geometric resolution: Compared to Flow3D's FAVOR approximation technique, this invention uses a body-fitted mesh, which can accurately resolve the sharp edges and twisted surfaces of the stirring blades, thereby accurately predicting stirring torque and power consumption.

[0019] More realistic rheological simulation: The introduction of the regularized Bingham model not only solves the numerical divergence problem in the low shear zone, but also accurately captures the distribution of the stirring blind zone (dead zone), providing a reliable basis for optimizing the blade arrangement design.

[0020] Computational efficiency optimization: By using nested topology, the huge computational overhead caused by global mesh reconstruction (Remeshing) is avoided, and the simulation cycle is significantly shortened while ensuring accuracy. Attached Figure Description

[0021] Figure 1 The diagram shows the configuration of the stirring head device and the corresponding stirring head structure.

[0022] Figure 2 The diagram shows the structure of the agitator head captured by Flow3D.

[0023] Figure 3 The diagram shows that the complete computational domain consists of two independent regions.

[0024] Figure 4 A schematic diagram of the motion computation domain is shown.

[0025] Figure 5 A schematic diagram of the complete computational domain is shown.

[0026] Figure 6 The diagram shows the left and right cutter head models of the geometric model of the curing agent mixing equipment.

[0027] Figure 7 This diagram shows a partial model of the pipeline nozzles and support structure of the curing agent mixing equipment.

[0028] Figure 8 This diagram shows the overall model of the pipeline nozzles and support structure of the curing agent mixing equipment.

[0029] Figure 9 A schematic diagram of the AIM boundary range near the agitator head is shown.

[0030] Figure 10 The grid distribution near the stirring head is shown.

[0031] Figure 11 The overall grid layout of the computational region is shown.

[0032] Figure 12 A model diagram of a single-outlet inclined blade device is shown.

[0033] Figures 13-19 The diagram shows the distribution of the curing agent in the xz plane during the operation of a single-outlet inclined blade device.

[0034] Figures 20-26The diagram shows the distribution of the curing agent in the yz plane during the operation of a single-outlet inclined blade device.

[0035] Figure 27 The flowchart of the motion coupling solution method for a mixer based on ACMI and AMI is shown. Detailed Implementation

[0036] Various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0037] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0038] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0039] Numerical model A multiphase fluid-structure interaction numerical model of the mixing head, mud, and solidifying agent was established based on the open-source computational fluid dynamics library OpenFOAM. A two-phase flow mixing model was used to simulate the mixing process of the mud and solidifying agent, treating the mixed mud and solidifying agent as incompressible fluids. The governing equations are as follows: (1) (2) In the formula, It is the velocity field in rectangular coordinates. It's density. It is the total pressure. It is gravitational acceleration. It is the dynamic viscosity of the mixed fluid. It is the turbulent Reynolds stress tensor. The superscript T indicates the transpose of the vector.

[0040] This model uses the Volume of Fluid (VOF) method to simulate the mixing process of mud and solidifying agent within the computational region. The VOF method defines a variable... This is used to represent the phase fraction of the fluid. Consider a two-phase system of mud and solidifier in a certain grid cell; if this grid cell is filled with solidifier, then... If this grid cell is filled with mud, then If If the value is between 0 and 1, then the grid cell contains a mixture of mud and curing agent. The change is affected by the velocity field within the flow field The influence of this is reflected in the motion control equation: (3) According to the definition of the VOF method in formula (3), the fluid velocity in formulas (1) and (2) is... ,density and molecular kinematic viscosity With volume fraction The changes are as follows: (4) (5) (6) In this context, subscript 1 represents the curing agent phase, and subscript 2 represents the mud phase.

[0041] It is worth noting that general models typically simplify mud as a concentration-dependent Newtonian fluid. However, soil mud and solidifying agent solutions generally contain fine clay particles, and their mixtures often exhibit non-Newtonian fluid characteristics with strong yield stress. Their viscosity changes with the shear strain rate during stirring. To accurately simulate the rheological characteristics of mud and solidifying agent solutions during stirring and diffusion, this model uses the Bingham-Papanastasiou model to characterize the viscosity changes of mud or solidifying agent solutions under different strain rate conditions. (7) In the formula This represents high shear viscosity. The parameter m represents the magnitude of the yield stress, indicating the increase in yield stress under low shear rate conditions. In this simulation, m = 2.0. Represents the shear strain rate tensor. It is related to the density of the mud or hardener solution and represents the volume fraction of solids in the solution. Specific parameters can be calculated based on the on-site measured density or concentration data of the mud / hardener.

[0042] In formula (2) This is the turbulent Reynolds stress tensor, and a suitable turbulence model is needed to close the turbulence terms in the equations. In this model, the k-ω SST model is chosen for turbulence closure because it can better predict boundary layer separation flow under the influence of the reverse pressure gradient. Its governing equations are: , In the formula For the turbulent kinetic energy generation term, the parametric equations in equations (8) and (9) are as follows: , In the formula, The parameter in equation (11) represents the distance from a grid point to the nearest wall. The parameters in equation (12) They are defined as follows: , In formula (8) This is the buoyancy correction term, representing the effect of fluid density variations within the flow field on the generation of turbulent kinetic energy. This buoyancy correction term is primarily influenced by the density gradient and turbulent viscosity. According to the standard gradient diffusion hypothesis, the buoyancy correction term is defined as follows: , in The Prandtl number is turbulent, and its value in this paper is taken as 0.85. The parameter in equation (9) is defined as: Defined as: , In the formula , , and These represent the magnitude of the horizontal flow velocity and the magnitude of the vertical flow velocity, respectively.

[0043] according to k - ω The SST model is defined, and its model parameters are determined according to the relationship in equation (17) from... Model and The constant parameters derived from the model are shown in Table 1.

[0044] , Table 1 Turbulence Model Parameters .

[0045] Motion control methods: The mixing equipment for curing agents involves a complex coupled process of the rotational motion of the agitator head and the overall vertical translational motion. Simulating long-distance displacements or large-scale structural motions has always been a technical challenge in fluid-structure interaction (FSI) simulations based on meshed methods such as CFD. Taking the downward movement of the mixing equipment as an example, using a dynamic mesh simulation algorithm based on traditional local mesh deformation methods inevitably leads to excessive compression of the mesh in front of the mixing equipment's direction of movement and excessive stretching of the mesh behind it. Excessive compression and stretching of the mesh degrades mesh quality, further resulting in computational instability or decreased simulation accuracy. Furthermore, the rotational motion of the agitator head needs to be coupled and simulated during translational motion, further increasing the complexity of the simulation.

[0046] In recent years, with the development of new dynamic mesh algorithms, necessary technical support has been provided for simulating long-distance displacement or large-scale mesh deformation problems, such as the overset algorithm. In an overset algorithm, there are generally at least two sets of meshes, one of which contains the other. The two sets of meshes are independent of each other, and the motion process of each set can be controlled separately. The governing equations are solved separately in the two sets of meshes, and key flow field parameters are exchanged through interpolation between some mesh points in the overlapping regions of the background and overset meshes. Different interpolation weights are derived based on the relative distance between the interpolated mesh points. Because the relative positions of the two sets of meshes change continuously during the calculation, the interpolated mesh points also change continuously. Therefore, it is difficult to meet the conservation requirements of the governing equations in the simulation using the overset algorithm. Thus, the overset algorithm places high demands on the topology and mesh quality of both sets of meshes. However, the configuration of a curing agent mixing device is very complex. To accurately characterize the integrated characteristics of the various parts of the mixing device, the resulting body-fitted mesh is difficult to meet the mesh quality requirements in the overset simulation process. When the mesh quality is poor, the overlapping mesh algorithm cannot accurately identify the correspondence between mesh interpolation points in complex motion processes such as rotation and translation, resulting in poor computational stability and a high likelihood of divergence.

[0047] To address the aforementioned problems, this invention innovatively proposes a dynamic meshing method based on the coupling of the Arbitrary Coupled Mesh Boundary (ACMI) algorithm and the AMI sliding boundary algorithm. This method can effectively simulate the complex coupled motion process of the blade rotation and overall translation in a curing agent mixing device. The ACMI boundary algorithm uses only one mesh, but this mesh contains different computational regions connected by the ACMI boundary. For example... Figures 3-4As shown, in this invention, the complete computational domain consists of two independent regions: a static region and an intermediate moving region. The static region is hollow. The four sides inside the hollow region and the four sides outside the moving region have identical coordinates in the x and y directions, respectively. Thus, the two independent computational regions can be combined to form a complete computational domain, as shown below. Figure 5 As shown in the diagram, there are two pairs of overlapping boundaries within the complete computational domain; these two pairs of boundaries are the ACMI boundaries. In this invention, the moving region in the middle can slide along the ACMI boundaries as a whole. To ensure that the moving region and the stationary region always form a complete computational domain during the sliding process, the length of the moving region must be longer than that of the stationary region. During the sliding of the moving region along the ACMI boundaries, there are constantly changing coupling and non-coupling surfaces on the ACMI boundaries (coupling surfaces are the surfaces that contact each other between the moving and stationary regions, while non-coupling surfaces are the surfaces that do not contact each other). Interpolation exists between data from different regions on the coupling surfaces, while on the non-coupling surfaces, it is equivalent to wall boundary conditions.

[0048] In addition to using the ACMI algorithm to simulate the long-distance translational motion of the stirring equipment, the AMI algorithm is also needed to simulate the rotational motion of a local area of ​​the agitator head, while simultaneously superimposing the translational motion process onto the rotational region. The AMI algorithm is a numerical technique for simulating unsteady flow in rotating machinery, particularly suitable for handling relative motion problems between rotating and stationary regions. This approach divides the computational domain into rotating and stationary regions, with a completely overlapping but distinct interface between them. Data exchange between the different regions is achieved through interpolation at the interface. Based on the motion control method, the specific model settings are as follows.

[0049] Modeling process 1. Structural Preprocessing. Based on existing mixing equipment drawings, digital modeling of the mixing equipment was performed using 3D modeling software such as Rhino. During the modeling process, to facilitate subsequent mesh generation and control of the movement in different areas, the mixing equipment was divided into three parts according to its movement (as shown in Figure 5): the left and right agitator heads (involving rotational and translational motion), and the middle section consisting of the fixed support and nozzle piping (involving only translational motion). During the segmentation modeling process, it was necessary to ensure that the left and right agitator heads and their supporting structures could fit perfectly (the planes had the same center position, radius, and tilt angle). All faces on the left and right agitator head structures in the model could form complete closed solids, and the solids of the left and right agitator heads were exported in STL file format, named rotate_left and rotate_right respectively. The entire piping nozzle and supporting structure also needed to be exported as an STL file, but the faces at the piping nozzles needed to be named INLET so that they could be identified as inflow boundaries during later mesh generation. One feasible approach is to first export the parts other than the nozzle faces in ASCII encoding, naming them "other". Then export the individual nozzle surfaces in ASCII encoding format and name them INLET. Finally, you can open both STL files with Notepad or an ASCII text editor, copy all the contents of the INLET file to the other file, and save it.

[0050] In addition, to construct both rotating and non-rotating regions during mesh generation, a pair of cylindrical AMI sliding mesh boundaries (such as...) are also added near the agitator head during modeling. Figure 9 As shown, the sliding mesh boundary is slightly larger than the area of ​​the swivel head, completely encompassing the swivel head within the sliding boundary. The two AMI boundaries also need to form a closed solid and be exported as STL files, named AMI_left and AMI_right respectively.

[0051] 2. Computational Mesh Generation. The computational mesh generation requires separate generation of meshes for the moving region and the stationary region. When generating the moving region mesh, the geometric dimensions of the mixing equipment should be considered. In the xy direction, the mesh region must completely encompass the mixing equipment, which can be extended outwards by 0.1D (D is the diameter of the generated AMI boundary entity) from the outermost edge of the mixing equipment's vertical projection dimension. In the z direction, the top of the mesh computational region must completely encompass the top of the mixing equipment, and the bottom must align with the stationary region mesh. Initially, the bottom of the moving region mesh and the bottom of the stationary region mesh should be on the same horizontal plane. The background mesh of the moving region is initially divided using the `blockMesh` command in OpenFOAM. The mesh can be a hexahedral mesh with a cell size of 0.05D. During mesh generation, the generated background mesh region can be set as a `cellZone` and given a name (e.g., C3Zone) to facilitate subsequent control of its movement through different `cellZone`s. After generating the background mesh, all previously generated STL files are placed in the constant / triSurface path within the example directory. The snappyHexMesh command in OpenFOAM is then used to mesh the area near the mixing device. Before running the snappyHexMesh command, relevant parameters need to be set in its control dictionary file (system / snappyHexMeshDict). The main modifications are as follows: disable the command to add boundary layers; add recognition for INLET surfaces in the other.stl file and name them "inlet boundary," specifying the boundary type as "patch"; use the STL files of two AMI boundaries to segment the computational domain, setting the regions inside the two boundary surfaces as dynamic domains, and also setting cellZones for the two dynamic domains, which can be named C1Zone and C2Zone. Based on these specific settings, running the snappyHexMesh command will generate the computational domain mesh for the dynamic domain.

[0052] For the static region, the mesh can be generated using software such as Pointwise. It needs to be a hollow cube structure, and its boundary scale can be set according to the required simulation range. It is important to note that the internal boundary of the hollow part must coincide with the external boundary of the moving region, and the mesh scale near the hollow region should be similar to the mesh scale on the boundary of the moving region to ensure accuracy during data exchange. To reduce computational cost, the mesh distribution in the xy-plane can gradually change from denser in the hollow area to sparser at the outside.

[0053] After the meshes for both the moving and stationary regions are generated, the mergeMesh command in OpenFOAM can be used to merge the meshes of the moving and stationary local regions into a complete computational domain. Figures 10 and 11 show the mesh near the stirring head generated by snappyHexMesh and the total mesh distribution of the merged computational domain, respectively.

[0054] 3. Motion Control. The multiSolidBodyMotionSolver in OpenFOAM can be used to solve for object motion and achieve motion control for different cell zones in the model. For example, for C1 Zone and C2 Zone, their motion can be decomposed into a superposition of rotational and linear motions. The multiMotion method in solidBodyMotionFunction is used to implement the superposition of motions. The motion forms are divided into one and two: one is linear motion, requiring the specification of its velocity; two is rotational motion, requiring the specification of the rotation axis, origin, and angular velocity. Note that the rotation axis is the normal vector of the center of the agitator cylinder, and the origin must be any point on this normal vector. For C3 Zone, only linear motion control is needed, and its motion speed must be exactly the same as the motion speed of the rotating region.

[0055] 4. Run the solver. Set the initial and boundary conditions for the model (in folder 0). First, set the initial concentration field volume fraction to 0, indicating that the computational domain is entirely composed of mud at the initial moment. For the computational domain boundaries, the solid boundaries of the mixing equipment (stirring head, support structure, pipe sidewalls, etc.) need to be set to movingWallVelocity boundaries to account for flux differences caused by wall movement. For the nozzle location, it can be set as an inflow boundary, specifying the inflow volumetric flow rate or velocity, and the concentration field volume fraction at the nozzle boundary is set to 1. After setting, you can run the solver for the above model to solve it, or you can call the mpi command to solve the model in parallel across the computational domain.

[0056] Application example: Based on on-site engineering data, a simulation analysis was conducted on existing equipment with a single discharge port inclined blade, and its blade structure is as follows: Figure 12As shown, the mixing equipment rotates at 70-100 rpm during construction, with a maximum lifting speed of 2 m / min. The density of the soil slurry is approximately 1.85 g / cm³, and the dry density of the curing agent powder is 2.6 g / cm³. The curing agent powder and water are mixed at a weight ratio of 0.8:1 to form a curing agent solution, with a density of approximately 1.38 g / cm³. Calculations show that the solid volume fraction ϕ in the soil slurry is 0.515, and the solid volume fraction ϕ in the curing agent solution is 0.23. Substituting these parameters into Formula 7 yields the yield stress and high shear viscosity for different terms, as shown in Table 2.

[0057] Table 2 Model viscosity parameters , Based on the geometric model of the mixing device established by the above method, a spatial discrete model of the computational region is established. The lengths of the stationary region along the (x, y, z) direction are (10m, 10m, 5m), and the lengths of the moving region along the (x, y, z) direction are (3m, 3m, 11.5m). The mixing device is located in the middle of the moving region, and at the initial moment, the mixing head is located at the top of the stationary region. At this time, the bottom boundary of the stationary region and the bottom boundary of the moving region are at the same height.

[0058] In this simulation, the rotation speed of the agitator head is set to 100 rpm, the lifting speed is 2 m / min (0.03333 m / s), the equipment starts moving with a downward and then upward motion, the duration of the downward and upward motion processes is 90 s, and the nozzle volumetric flow rate is 0.013 m3 / s.

[0059] Figures 13-19 and Figures 20-26 The distribution of the curing agent in the xz and yz planes during the operation of a single-outlet inclined blade device is shown in Figure 11. The blue grid lines represent the mixing equipment, the red area is the isosurface with an equivalent curing agent volume fraction of 0.06, and the top coordinate of the z-axis (-3) represents the upper boundary surface of the soil slurry. From the xz plane distribution changes shown in Figure 11, it can be observed that during the device's descent, the curing agent is mainly distributed near the two blades, and after a period of time, it forms an approximately symmetrical strip-like distribution along the device's central axis (e.g., ...). Figure 16 (As shown in the diagram). During the equipment rising phase, the distribution range of the curing agent changes little in the z-direction, while the distribution range in the x-direction expands significantly. Furthermore, due to the disturbance during the equipment rising process, the symmetrical distribution characteristics near the two agitator heads are weakened.

[0060] Figures 13-19The diagram shows the distribution of the curing agent in the xz plane during the operation of a single-outlet inclined blade device (the time interval between two adjacent images is 30 seconds). The blue grid lines represent the mixing equipment, the red area is the isosurface with an equivalent curing agent volume fraction of 0.06, and the top coordinate of the z-axis (-3) represents the upper boundary surface of the soil slurry. Depend on Figures 20-26 (The time interval between two adjacent images is 30 seconds.) The changes in the yz-plane distribution reveal that during the equipment's descent, the curing agent is mainly and evenly distributed on both sides of the cutter head within a range from -0.8m to 0.8m, with the height of the distribution area gradually extending as the cutter head descends. During the equipment's ascent, the distribution range of the curing agent in the z-direction also changes relatively little, while the distribution range along the positive y-axis expands significantly.

[0061] Figures 20-26 The diagram shows the distribution of curing agent in the yz plane during the operation of a single-outlet inclined blade device. The blue grid lines represent the mixing equipment, the red area is the isosurface with an equivalent curing agent volume fraction of 0.06, and the top coordinate of the z-axis, -3, represents the upper boundary surface of the soil slurry.

[0062] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for solving the motion coupling of a mixer based on ACMI and AMI, characterized in that, The method includes: Based on the existing drawings of the mixing equipment, a digital model of the mixing equipment is created using 3D modeling software. The AMI algorithm is used to simulate the rotational motion of a local area of ​​the agitator head; The simulation of long-distance translational motion of a stirring device is achieved using the ACMI algorithm, including: determining the complete computational domain, which consists of two independent regions: a stationary region and an intermediate moving region. The stationary region is hollow. Computational mesh generation: Generate meshes for the moving region and the stationary region respectively; Motion control: The multiSolidBodyMotionSolver in OpenFOAM is used to solve the object motion problem and achieve motion control for different grid zones in the model. The initial and boundary conditions of the model are set, and the model is run to solve for the spatial distribution and concentration of the curing agent. The initial conditions include the volume fraction of the concentration field at the initial moment, and the boundary conditions include: the inlet boundary, the outlet boundary, and the solid boundary of the stirring device.

2. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 1, characterized in that, Based on existing mixing equipment drawings, a digital model of the mixing equipment is created using 3D modeling software, including: During the modeling process, the mixing equipment was divided into three parts according to its motion: the left and right blades, the middle part, and the fixed support and nozzle pipeline. During the segmentation modeling process, it is necessary to ensure that the left and right sides of the swivel head and its supporting structure are completely fitted, that is, the planes of the two sides of the swivel head and its supporting structure have the same center position, radius and tilt angle. Ensure that all faces on the left and right cutter head structures in the model can form a complete closed solid, and export the solids of the left and right cutter heads in the format of STL file, named rotate_left and rotate_right respectively; The entire pipeline nozzle and support structure also need to be exported as an STL file. The surface at the pipeline nozzle should be named INLET so that the surface at the pipeline nozzle can be identified as the inflow boundary when meshing later. The agitator head involves rotational and translational motion, while the fixed bracket and nozzle piping involve translational motion.

3. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 1, characterized in that, Based on existing mixing equipment drawings, a digital model of the mixing equipment is created using 3D modeling software, which also includes: First, export the parts other than the nozzle surface in ASCII encoding and name them "other". Then export the individual nozzle surfaces in ASCII encoding format and name them INLET; Open both STL files using Notepad, an ASCII text editor, and copy all the contents of the INLET file to the 'other' file and save it.

4. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 3, characterized in that, Based on existing mixing equipment drawings, a digital model of the mixing equipment is created using 3D modeling software, which also includes: In order to construct the rotating and non-rotating regions during the meshing process, a pair of cylindrical AMI sliding mesh boundaries need to be added near the swivel head during modeling. The range of these sliding mesh boundaries is slightly larger than the range of the swivel head, so that the swivel head can be completely included within the sliding boundary. The two AMI boundaries also need to form a closed solid and be exported as STL files, named AMI_left and AMI_right respectively.

5. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 1, characterized in that, Computational grid generation includes: When generating the mesh for the moving region, the geometric dimensions of the mixing equipment can be used to determine the mesh area to completely include the mixing equipment in the xy direction. This can be achieved by extending the outermost edge of the vertical projection dimension of the mixing equipment by 0.1D (where D is the diameter of the generated AMI boundary entity). In the z direction, the top of the mesh calculation area needs to completely include the top of the mixing equipment, and the bottom needs to match the mesh of the stationary region. Initially, the bottom of the mesh in the moving region and the bottom of the mesh in the stationary region are on the same horizontal plane.

6. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 1, characterized in that, Computational grid generation also includes: The background mesh of the motion region is initially divided using the blockMesh command in OpenFOAM. The mesh can be a hexahedral mesh with a cell size of 0.05D. When dividing the mesh, the generated background mesh region is set as a cellZone and given the name C3Zone, which is used to control its motion process through different cellZones later. After the background mesh is generated, all the previously generated STL files are placed in the constant / triSurface path in the example directory, and the snappyHexMesh command in OpenFOAM is used to mesh the area near the mixing device. Before running the snappyHexMesh command, set the relevant parameters in its control dictionary file. The main operations that need to be modified are as follows: disable the command to add boundary layers; add recognition of the INLET surface in the other.stl file and name it the inlet boundary, and give the boundary type as patch; use the STL files of two AMI boundaries to divide the computational region, set the region inside the two boundary surfaces as the dynamic domain, and set cellZone for the two dynamic domains, naming them C1Zone and C2Zone. Running the snappyHexMesh command will generate the computational domain mesh for the dynamic domain; The path to the control dictionary file is system / snappyHexMeshDict.

7. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 6, characterized in that, Computational grid generation also includes: For the mesh of the static region, the pointwise software is used to generate it. The static region is a hollow cube structure, and its boundary scale range can be set according to the range to be simulated. The internal boundary of the hollow part of the stationary area needs to coincide with the external boundary of the moving area, and the grid scale near the hollow area needs to be similar to the grid scale on the boundary of the moving area to ensure accuracy during data exchange. To reduce computational cost, the distribution of the grid in the static region on the xy plane is a gradual change from denser in the hollow areas to sparser at the outside. After the meshes for both the moving and stationary regions are generated, the mergeMesh command in OpenFOAM is used to merge the meshes of the moving and stationary regions into a complete computational domain.

8. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 1, characterized in that, Computational grid generation also includes: Motion control includes: For C1Zone and C2Zone, their motion is decomposed into a superposition of rotational motion and linear motion; The multiMotion method in solidBodyMotionFunction is used to implement superimposed motion.

9. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 1, characterized in that, Computational mesh generation also includes: dividing the motion form into one and two. One is linear motion, which requires specifying its motion speed; two is rotational motion, which requires specifying the rotation axis, rotation origin, and rotational angular velocity. The rotation axis is the normal vector of the center of the cylinder of the agitator head, and the rotation origin must be any point on this normal vector. For C3Zone, only linear motion control is required, and its motion speed needs to be exactly the same as the linear motion speed of the rotating area.

10. The method for solving the motion coupling of a mixer based on ACMI and AMI according to claim 1, characterized in that, The initial and boundary conditions of the model are set, and the solution is run to obtain the spatial distribution and concentration of the curing agent, including: First, the volume fraction of the concentration field at the initial moment is set to 0, which means that the calculation area at the initial moment is all mud. For the computational domain boundary, the solid boundary of the mixing device needs to be set to the movingWallVelocity boundary to account for the flux difference caused by wall movement; The movingWallVelocity boundary is a specific boundary condition already present in OpenFOAM, which ensures that the velocity of the fluid near the moving solid surface is the same as the velocity of the solid, so as to reach the no-slip boundary. For the nozzle location, set it as the inflow boundary, specify the inflow volumetric flow rate or velocity, and set the concentration field volume fraction at the nozzle boundary to 1; after setting, run the solver of the above model to solve it, or call the mpi command to solve the model in parallel over the computational domain, including: The Bingham-Papanastasiou model was used to characterize the viscosity changes of mud or solidifying agent solutions under different strain rates. The k-ω SST model, modified by the buoyancy term, was used for turbulence closure and was used to predict boundary layer separation flow under the influence of the reverse pressure gradient. The k-ω SST model is a model that considers the influence of the density change of the mixed fluid on turbulence generation. The solid boundaries of a mixing device include the agitator head, the support structure, and the boundaries of the pipe sidewalls.

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