CN106709180B - Numerical simulation method for PIM (plasma independent deposition) mold filling process of superfine hard alloy step round rod - Google Patents
Numerical simulation method for PIM (plasma independent deposition) mold filling process of superfine hard alloy step round rod Download PDFInfo
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Abstract
The invention relates to a numerical simulation method for a PIM (plasma independent deposition) mold filling process of an ultrafine hard alloy step round rod. By means of equivalent powder, a multi-fluid model, optimized fluid inlets and outlets, a grid model is refined, interaction of fluid pairs is reasonably set, convergence of a simulation process is effectively improved, the problem that calculation is easy to disperse due to large density difference, large viscosity difference, small interface interaction depth and the like of a binder and powder is solved, visualization of a feeding melt mold filling flowing process is achieved, mold filling characteristics such as respective speed, temperature and viscosity physical field distribution of the powder and the binder can be effectively mastered, a binder formula is optimized, critical powder loading is determined, and accordingly PIM (plasma independent multicast protocol) process is improved. The method can be used for inspecting the defects of air bubbles, collapse and the like in the mold filling process, analyzing the root cause and the influence factors of segregation, predicting the information of the defects of cracks, air holes, welding lines and the like, and providing useful information for analyzing the PIM process conditions and the feeding properties of the superfine hard alloy, guiding the process parameters and designing the mold.
Description
Technical Field
The invention belongs to the technical field of powder metallurgy near-net forming, and particularly relates to a numerical simulation method for a PIM (plasma independent deposition) mold filling process of a superfine hard alloy step round rod.
Background
Because of its high strength, hardness and wear resistance, the superfine WC-Co hard alloy is widely used in many fields such as tools, dies and wear-resistant parts, including metal cutting tools, wire drawing and stamping dies, sealing rings, nozzles, etc.
The superfine hard alloy Powder Injection Molding (PIM) not only can obtain the alloy with high strength, high hardness and high wear resistance, but also can prepare a near-net shaped product with a complex shape, and has the advantages which cannot be compared with the conventional powder metallurgy and machining method.
The mold filling process of powder injection molding is a non-isothermal, non-stationary complex flow of a non-newtonian fluid, which is a multi-phase flow process comprising powder particles in a solid phase, a binder in a liquid phase, and a gas in a mold cavity. Because the superfine WC/Co mixture has particle agglomeration, the tap density is only 25-40% of the theoretical density; powder agglomerated particles still exist in the superfine WC/Co feed, the WC/Co particles are not sufficiently wrapped by the binder, the thermal stability of the feed is low, the reduction range of the flowability of the superfine feed is reduced to 60 percent at most due to the powder agglomeration, the production process is difficult to control effectively, and the cost of experimental research is high. With the development of computer technology, for the repeated debugging and correcting process in the traditional die production, the numerical simulation can effectively optimize the process parameters, improve the die quality and reduce the production cost. At present, no relevant report of numerical simulation of the mold filling process of the ultrafine hard alloy injection molding is found.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a numerical simulation method for a PIM (plasma independent deposition) mold filling process of an ultrafine hard alloy step round rod.
The technical scheme adopted by the invention is as follows:
a numerical simulation method for a PIM mold filling process of an ultrafine hard alloy step round rod comprises the following steps:
1) simplifying a model of the step round rod, setting a mold filling inlet and a mold filling outlet, and establishing a three-dimensional geometric model of the step round rod;
2) carrying out mesh division on the step round bar three-dimensional geometric model in the step 1) and establishing a finite element model;
3) physically defining the finite element model in the step 2), and assuming and simplifying a gas-liquid-solid multiphase flow mold filling flowing process in a cavity according to an operation environment of on-site ultrafine hard alloy injection molding and under the condition of not influencing calculation accuracy, wherein the specific setting is as follows:
(a) define multi-stream phase material: the WC/Co mixture, the binder mixture and the air are named as powder, binder and air respectively, and the parameters of the powder, the binder and the air are defined respectively, wherein the parameters comprise thermodynamic state, molar mass, theoretical density, specific heat, viscosity and heat conduction coefficient;
(b) defining a simulation type: selecting unsteady state simulation, and setting time parameters;
(c) defining a multiphase fluid domain: creating a domain for the step round bar, and defining a fluid model and fluid detailed information;
(d) defining boundary conditions: the method comprises the boundary conditions of a mold filling inlet (inlet), a mold filling outlet (outlet) and a mold wall (wall), and specific boundary conditions are respectively given; setting initial values including temperature and pressure in the die cavity, and respective speeds and volume fractions of powder, binder and air in the die cavity;
(e) setting solution control: selecting a divalent backward Euler formula to solve the precision, wherein the physical variables comprise viscosity, pressure, speed, temperature, density, heat flow and volume fraction;
4) and (3) numerical simulation calculation: solving by adopting a finite volume method, and timely checking problems existing in calculation and/or checking the accuracy degree of the solution through residual errors and solving information;
5) performing visual analysis on the convergence simulation calculation result to obtain the powder in the mold filling process,
The respective speed distribution, temperature distribution, pressure distribution, volume fraction distribution and viscosity distribution of the binder and the air, the influence of process parameters on the mold filling process is analyzed, the binder formula is optimized, and the feeding critical powder loading capacity of the WC/Co mixture is determined.
In the step 1), an actual sprue of a mold cavity is taken as a mold filling inlet, and a far end of the sprue is taken as a mold filling outlet.
And 2) adopting non-structural tetrahedral mesh division in the step 2), wherein the size of the global mesh is 0.2mm, the inner wall of the die cavity, the inner wall of the die filling inlet and the inner wall of the die filling outlet are in the shape of circular arcs, and after the tetrahedral mesh is generated, the triangular prism mesh is used for refining the edges of the circular arcs, and the quality of the mesh is tested to reach 0.4, so that the calculation requirement is met.
In the step 3) (a), the WC powder granularity of the WC/Co mixture is 0.2-0.6 μm, and the mass percentage content of Co is 6-15%; the material parameters of the binder are obtained by theoretical calculation, reference or actual measurement.
In step 3) (b), the total duration is set to 0.05s and the time step is set to 5X 10-5s, initial time 0 s.
In STEP 3) (c), creating a domain for the STEP round BAR, and naming the domain as STEP BAR; starting the buoyancy model, wherein the buoyancy reference density is 1.185g cm-3(ii) a The reference pressure of the domain model is 1 atm; the buoyancy model is Buoyant, the gravity acceleration in the Y direction is-g, and the gravity acceleration in the X, Z direction is 0 m.s-2The buoyancy reference density is set to the density of the less dense phase of the three phases, i.e., the air density; the domain is set to be static; no deformation of the grid.
In the step 3) (c), the multiphase option in the fluid simulation is set to be heterogeneous, the heat transfer model is set to be enthalpy energy, and the turbulent flow model is set to be a laminar flow model.
In the step 3) (c), the interphase transmission of the fluid pairs (air | binder) and (air | powder) in the fluid simulation are both free surface models, and the surface tension coefficient is set to be 0.072 N.m-1Drag coefficient of 0.44Pa-1·s-1No material transport; the fluid pair (binder | powder) is transmitted in phase to form a mixed model, the interface interaction depth is set to be 0.2-0.6 μm, and the drag force coefficient is 0.44Pa-1·s-1～14.4Pa-1·s-1。
In the step 3) (d), the boundary conditions of the filling inlet (inlet) are that the fluid is set to be subsonic, and the mass and the momentum are set to be standard speed of 0-20 m.s-1The heat transfer is set to a static temperature of 423K, and the volume fractions of powder, binder and air in the fluid values are respectively
Wherein the content of the first and second substances,
the boundary conditions of the mold filling outlet (outlet) are that the fluid is set to be subsonic, the mass and momentum are set to be average static pressure,the relative pressure is 0Pa, and the mixing factor is 0.05; the die Wall (Wall) boundary conditions were set to no slip and the heat transfer temperature was 298K.
In step 3) (d), initial value setting: given T equal to 0, the temperature T equal to 298K in the mold cavity, the pressure P equal to 1atm, and the velocities v of the powder, the binder and the airp＝vb＝va0.0001m/s, volume fraction of air
The volume fraction of powder and binder is
In step 3) (e), the minimum step number and the maximum step number are calculated as 1 step and 100 steps in convergence control, and the convergence scheme is that the root mean square residual value RMS is 1 × 10-4The transient time step is 10 steps.
In step 4), a powder-binder multi-fluid model based on a finite volume method is adopted for numerical simulation, and powder particles and a binder belong to two fluids which are independent and interact with each other on the assumption that the powder particles and the binder are continuous media which coexist and can mutually permeate at any spatial position.
Further, in the multi-fluid model, when no phase change occurs at a phase interface, no mass exchange exists between two phases, and a pulsation term is ignored, so that the two-phase flow mass, momentum and energy conservation equation obtained by an averaging method is met, the Reynolds number in the PIM filling flow process is small, Nu is approximately equal to 2, and the dragging force of the PIM filling flow model is a mixed model.
The invention has the beneficial effects that:
according to the invention, through equivalent powder, a multi-fluid model, optimized fluid inlet and outlet, a grid model refinement and reasonable setting of fluid pair interaction, the convergence of a simulation process can be effectively improved, the difficult problems of easy divergence of calculation caused by large density difference, large viscosity difference, small interface interaction depth and the like of the binder and the powder are solved, the visualization of a feeding melt mold filling flowing process is realized, the mold filling characteristics of the powder and the binder such as respective speed, temperature and viscosity physical field distribution and the like can be effectively mastered, the binder formula is optimized, the critical powder loading capacity is determined, and the PIM process is improved. The method can be used for inspecting the defects of air bubbles, collapse and the like in the superfine hard alloy feeding and mold filling processes, analyzing the segregation generation source and the influence factors thereof in the mold filling process, predicting the defect generation information of cracks, air holes, welding lines and the like in the PIM mold filling process, and providing useful information for analyzing the PIM process conditions and the feeding properties of the superfine hard alloy, and guiding process parameters and mold design.
The simulation process and the result of the invention are easy to compare with the experimental result, the model calculation amount is small, the initial condition is easy to be given and the obtained result is easy to be applied.
Drawings
FIG. 1 is a schematic diagram of (a) UG model and (b) finite element model of an ultrafine WC/10Co cemented carbide PIM mold-filling mold cavity in an embodiment.
FIG. 2 is a graph showing the variation of the volume fraction distribution of the feed melt and the powder temperature distribution on the central plane perpendicular to the gate during the filling of the ultrafine WC/10Co feed mold.
Fig. 3 is a velocity difference plot of the binder and powder on the longitudinal center line when the PIM of the ultra-fine WC/10Co cemented carbide in the example is filled for 0.03s, wherein the powder loading is 49% and the gate is at the position where Z is 31 mm.
Fig. 4 is a graph showing the influence of the powder loading on the volume fraction distribution of (a) binder and (b) powder along the gate direction during the PIM mold filling process of the ultrafine WC/10Co cemented carbide in the example, where X is 2.8mm at the gate.
FIG. 5 is a graph of the effect of powder loading on the volume fraction distribution of powder and binder (horizontal cross section at the gate) in the examples.
FIG. 6 is a graph of the effect of different powder loadings on the performance of WC-10Co alloys: (a) hardness and bending strength; (b) density; (c) relative magnetic saturation.
Detailed Description
The invention is further described with reference to the following figures and detailed description. It should be emphasized that the following description is merely exemplary in nature and is not intended to limit the scope of the invention or its application.
Taking numerical simulation of the PIM mold filling process of the superfine WC/10Co hard alloy as an example, the numerical simulation method of the PIM mold filling process of the superfine hard alloy step round rod is explained. The method is implemented according to the following steps:
1) establishing a finite element model: a) simplifying a model of the step round bar, establishing a step round bar three-dimensional geometric model which is a single-side outlet model for the mold cavity by using a three-dimensional drawing software UG NX5.0 and taking an actual sprue of the mold cavity as a mold filling inlet and a sprue far end as a mold filling outlet, and exporting an x _ t format file as shown in FIG. 1 (a); b) importing the file obtained in the step a) into ANSYSICEM CFD 13.0.0 software, dividing by adopting a non-structural tetrahedral mesh, wherein the size of the global mesh is 0.2mm, the inner wall of a die cavity, the inner wall of an inlet and the inner wall of an outlet are in a circular arc shape, thinning the edge of the circular arc by using a triangular prism mesh after the tetrahedral mesh is generated, meeting the calculation requirement by checking that the mesh quality reaches 0.4, exporting a file in a CFX5 format, and carrying out mesh analysis to obtain an optimal mesh numerical model; c) importing the file obtained in the step b) into finite element software ANSYS CFX 13.0 to obtain a finite element model, as shown in FIG. 1 (b).
2) Setting before a domain: the WC/Co mix, binder mixture and air are named powder, binder and air, respectively, and the respective parameters of powder, binder and air are defined, respectively. The simulated WC/Co mixture is a WC/10Co mixture, and the granularity of WC powder is 0.6 mu m; the adhesive mixture consists of paraffin, a low-molecular coupling agent and a high-molecular polymer, and the adhesive mixture comprises the following components in percentage by mass: the wax is special wax for hard alloy, and accounts for 63 percent in total; the high molecular polymer is high-density polyethylene, polypropylene and low-density polyethylene, and accounts for 30 percent of the total weight; the low molecular coupling agent is stearic acid and dioctyl phthalate, and accounts for 7 percent of the total. The thermodynamic state of the powder is Liquid, the thermodynamic state of the binder is Liquid, the thermodynamic state of the air is Gas, and the main material parameters are shown in table 1.
TABLE 1 WC/10Co and Binder physical Properties parameters
▲Is a theory ofCalculating or assuming a value;#is an actual measured value; reference values.
3) Defining a simulation type: selecting unsteady state simulation, setting total duration of 0.05s and time step of 5 × 10- 5s, initial time 0 s.
4) And (3) generating a domain: creating a domain for the STEP round BAR, named STEP BAR; starting the buoyancy model, wherein the buoyancy reference density is 1.185g cm-3(ii) a The reference pressure of the domain model is 1 atm; the buoyancy model is Buoyant, the gravity acceleration in the Y direction is-g, and the gravity acceleration in the X, Z direction is 0 m.s-2The buoyancy reference density is set to the density of the less dense phase of the three phases, i.e., the air density; the domain is set to be static; no grid deformation exists; the multi-phase option in the fluid simulation is set to be heterogeneous, the heat transfer model is set to be enthalpy energy, and the turbulence model is set to be a laminar flow model. In the fluid simulation, the inter-phase transfer of the fluid pairs (air) and (air) is a free surface model, and the surface tension coefficient is set to be 0.072 N.m-1Drag coefficient of 0.44Pa-1·s-1No material transport; the fluid pair (binder | powder) is transmitted in a mixed mode, the interface interaction depth is set to be 0.2 mu m, and the drag force coefficient is 3.6Pa-1·s-1。
5) Defining boundary conditions: the boundary conditions of the ultra-fine WC/10Co feeding PIM mold filling process are shown in Table 2, wherein the boundary conditions are set
Respectively 0.49, 0.53, 0.57, 0.61 (corresponding to
0.51, 0.47, 0.43, 0.39 respectively), and different powder loadings were examined (c
49%, 53%, 57% and 61%, respectively) on the WC/Co feed mold filling process to obtain reasonable powder loading.
TABLE 2 PIM Filler Process boundary conditions
Initial conditions for the ultra-fine WC/10Co feed PIM mold filling process are shown in Table 3.
TABLE 3 PIM Filler Process initial Condition values
6) Setting solution control: selecting a divalent backward Euler formula to solve the precision, wherein the minimum step number is calculated in the convergence control to be 1 step, the maximum step number is calculated to be 100 steps, and the convergence scheme is that the root mean square residual value RMS is 1 multiplied by 10-4The transient time step is 10 steps. The physical variables are selected from viscosity, pressure, velocity, temperature, density, heat flow and volume fraction of the binder and powder.
7) Outputting a numerical calculation file with the suffix name def, introducing into CFX-Solver to define simulation calculation, and adopting a powder-binder multi-fluid model based on a finite volume method, wherein powder particles and a binder belong to two fluids which are independent and interacted, and the powder particles and the binder are assumed to be coexisting continuous media which can mutually permeate at any spatial position.
In the multi-fluid model, when phase change does not occur at a phase interface, no mass exchange exists between two phases, a pulsation term is ignored, the equation of conservation of mass, momentum and energy of two-phase flow obtained by an averaging method is met, the Reynolds number in the PIM filling flow process is small, Nu is approximately equal to 2, and the dragging force of the PIM filling flow model is a mixed model.
And timely checking the problems existing in the calculation and/or checking the accuracy degree of the solution through the residual error and the solution information.
8) The simulation results were analyzed using CFD-Post 13.0. And performing visual analysis on the converged simulation calculation result to obtain respective speed distribution, temperature distribution, pressure distribution, volume fraction distribution and viscosity distribution of the powder, the binder and the air in the mold filling process, analyzing the influence of process parameters on the mold filling process, optimizing the binder formula and determining the feeding critical powder loading capacity of the WC/Co mixture.
9) And comparing the simulation calculation results under different working conditions with the experiment results to verify the reasonability of the model.
The volume fraction distribution of the feed melt and the variation of the powder temperature distribution on the central plane perpendicular to the gate during the filling of the ultrafine WC/10Co feed mold in this example are shown in FIG. 2. As can be seen from fig. 2, the temperature field, the distribution volume fraction, and the like of each of the binder, the powder, the air, and the like during the mold filling process can be analyzed by the numerical simulation of the mold filling process according to the present invention. Similarly, the filling characteristics of each phase in the feeding and filling process can be further analyzed through physical fields such as a speed field, a viscosity field, a density field and the like, and the generation reasons of defects such as bubbles, segregation and the like can be further analyzed. Therefore, the invention is beneficial to effectively mastering the respective mold filling characteristics of the powder and the binding agent, inspects the generation of defects such as air bubbles, collapse and the like in the process of feeding and mold filling the superfine hard alloy, and provides useful information for analyzing process conditions and feeding properties, guiding process parameters and designing a mold.
The velocity difference pattern of the binder and the powder on the longitudinal centerline of the ultrafine WC/10Co in this example when the mold is filled with the feed for 0.03s is shown in FIG. 3, wherein the powder loading is 49% and the gate is at the position where Z is 31 mm. The speed difference of the adhesive and the powder at the gate of the melt is large, the speed difference is reduced along with further mold filling, the speed difference of the adhesive and the powder is increased along with the increase of the speed difference after flowing into the narrow section, and the speed difference is increased along with the further increase of the flowing distance. Therefore, in the mold filling process, the longer the melt flow distance, the lower the speed of the binder and the powder, the larger the speed difference, the more serious the segregation phenomenon and the greater the phase separation tendency. Therefore, when the speed difference near the gate is close to that at the gate, the powder loading of the feeding material is the critical powder loading, so that the critical powder loading of the ultrafine cemented carbide WC/10Co can be determined through the numerical simulation of the mold filling process.
This example allows analysis of powder loading versus ultra-fine WThe influence of the volume fraction distribution of the binder and the powder along the gate direction during the PIM mold filling process of the C/10Co cemented carbide is shown in fig. 4 and 5, where X is 2.8mm at the gate. It can be seen that the volume fraction distribution of binder and powder is essentially the same for different powder loadings when
When the process is carried out, the distribution of the binder and the powder is most stable, namely the reasonable loading of the superfine WC/10Co feeding material is about 53 percent.
The reasonable loading capacity of the WC/10Co feed obtained by the method is 53 percent, is consistent with the experimental result, and the WC-10Co alloy has the best comprehensive performance when the loading capacity is 53 percent as shown in figure 6, so the numerical simulation method is reasonable, can effectively analyze the segregation generation source and the influence factors thereof in the mold filling process, and provides useful information for analyzing the process conditions and the feed property, guiding the process parameters and designing the mold.
Claims (11)
1. A numerical simulation method for a PIM (plasma independent deposition) mold filling process of an ultrafine hard alloy step round rod is characterized by comprising the following steps:
1) simplifying a model of the step round rod, setting a mold filling inlet and a mold filling outlet, and establishing a three-dimensional geometric model of the step round rod;
2) carrying out mesh division on the step round bar three-dimensional geometric model in the step 1) and establishing a finite element model;
3) physically defining the finite element model in the step 2), and assuming and simplifying a gas-liquid-solid multiphase flow mold filling flowing process in a cavity according to an operation environment of on-site ultrafine hard alloy injection molding and under the condition of not influencing calculation accuracy, wherein the specific setting is as follows:
(a) define multi-stream phase material: respectively naming WC/Co mixture, binder mixture and air as powder, binder and air, and respectively defining the parameters of the powder, the binder and the air;
(b) defining a simulation type: selecting unsteady state simulation, and setting time parameters;
(c) defining a multiphase fluid domain: creating a domain for the step round bar, and defining a fluid model and fluid detailed information;
starting a buoyancy model, wherein the buoyancy model is Buoyant, setting buoyancy reference density, reference pressure of a domain model and gravity acceleration in the direction of X, Y, Z, and setting the buoyancy reference density as air density; the domain is set to be static; no grid deformation exists;
in the fluid simulation, the alternate transmission of the fluid to the air | binder and the air | powder is a free surface model, and a surface tension coefficient, a dragging force coefficient and no mass transmission are set;
the fluid pair combiner | power is transmitted alternately to form a mixed model, and interface interaction depth and a dragging force coefficient are set;
(d) defining boundary conditions: the method comprises the following steps of respectively providing specific boundary conditions of a mold filling inlet, a mold filling outlet and a mold wall; setting an initial value;
(e) setting solution control: selecting a divalent backward Euler formula to solve the precision;
4) and (3) numerical simulation calculation: solving by adopting a finite volume method, and timely checking problems existing in calculation and/or checking the accuracy assumption of the solution through residual errors and solving information;
5) and performing visual analysis on the converged simulation calculation result to obtain respective speed distribution, temperature distribution, pressure distribution, volume fraction distribution and viscosity distribution of the powder, the binder and the air in the mold filling process, analyzing the influence of process parameters on the mold filling process, optimizing the binder formula and determining the feeding critical powder loading capacity of the WC/Co mixture.
2. The method according to claim 1, wherein in step 1), the actual gate of the mold cavity is used as the mold filling inlet, and the far end of the gate is used as the mold filling outlet.
3. The method according to claim 1, characterized in that in step 2) unstructured tetrahedral mesh partitioning is adopted, the size of the global mesh is 0.2mm, wherein the inner wall of the die cavity, the inner wall of the die filling inlet and the inner wall of the die filling outlet are arc-shaped, after the tetrahedral mesh is generated, the triangular prism mesh is used for refining the arc edge, and the quality of the mesh is checked to reach 0.4, so that the calculation requirement is met.
4. The method of claim 1, wherein in step 3) (b), the total duration is set to 0.05s and the time step is set to 5 x 10-5s, initial time 0 s.
5. The method of claim 1, wherein in STEP 3) (c), a domain is created for the stepped round BAR, named STEP BAR; the buoyancy reference density is 1.185 g-cm-3(ii) a The reference pressure of the domain model is 1 atm; the gravitational acceleration in the Y direction is-g, the gravitational acceleration in the X, Z direction is 0 m.s-2。
6. The method of claim 1, wherein in step 3) (c), the multiphase option in the fluid simulation is set to heterogeneous phase, the heat transfer model is set to enthalpy energy, and the turbulence model is set to laminar flow model.
7. The method of claim 1, wherein in step 3) (c), the surface tension coefficient is 0.072N-m-1Drag coefficient of 0.44Pa-1·s-1The interface interaction depth is 0.2-0.6 μm, and the drag coefficient is 0.44Pa-1·s-1～14.4Pa-1·s-1。
8. The method of claim 1, wherein in step 3) (d), the boundary conditions of the mold filling inlet are that the fluid is set to be subsonic, and the mass and momentum are set to be at a standard velocity of 0-20 m-s-1The heat transfer is set to a static temperature of 423K, and the volume fractions of powder, binder and air in the fluid values are respectively
Wherein the content of the first and second substances,
the boundary conditions of the mold filling outlet are setThe fluid is subsonic, the mass and the momentum are set as average static pressure, the relative pressure is 0Pa, and the mixing factor is 0.05; the die wall boundary conditions were set to no slip and the heat transfer temperature was 298K.
9. The method of claim 1, wherein in step 3) (d), the initial values set: given T equal to 0, the temperature T equal to 298K in the mold cavity, the pressure P equal to 1atm, and the velocities v of the powder, the binder and the airp＝vb＝va0.0001m/s, volume fraction of air
The volume fraction of powder and binder is
10. The method of claim 1, wherein in step 3) (e), the minimum number of steps and the maximum number of steps are calculated as 1 step and 100 steps in the convergence control, and the convergence scheme is that the root mean square residual value RMS is 1 × 10-4The transient time step is 10 steps.
11. The method according to claim 1, wherein in step 4), the numerical simulation uses a powder-binder multi-fluid model based on a finite volume method, and the powder and the binder belong to two fluids that are independent of each other and interact, assuming that the powder particles and the binder are a continuous medium that coexist and can interpenetrate at any position in space.
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