CN117875140B - Numerical simulation method for complex fluid-slender flexible particle interaction - Google Patents

Abstract

The invention provides a numerical simulation method of complex fluid-slender flexible particle interaction characteristics, which is based on the movement process of the slender flexible particles in the fused deposition molding process, uses a non-Newtonian Carreau model to represent the rheological property of a fused thermoplastic material, can well describe the change condition of the viscosity of the fused raw material along with the shear rate, uses an overlapped grid technology to realize the large-amplitude movement of the slender flexible particles in the fluid, fully considers the interaction between the non-Newtonian fluid and the slender flexible particles, can predict the deformation, the position and the gesture of the slender flexible particles, and accurately calculates the resistance coefficient, the lift coefficient and the moment coefficient of the particles. Provides an effective solving way for improving and optimizing design of fused deposition modeling equipment, and has important theoretical significance and practical value.

Description

Numerical simulation method for complex fluid-slender flexible particle interaction

Technical Field

The invention relates to a numerical simulation method for complex fluid-slender flexible particle interaction characteristics, belonging to the technical field of method inventions.

Background technique

Additive manufacturing technology, also known as 3D printing, is a technology that uses powdered metal or plastic and other bondable materials to construct objects by printing layer by layer. Fused deposition modeling technology is currently the most mature, simplest and most common 3D printing technology. The working principle of this technology is to heat the thermoplastic material to a molten state in the nozzle, and the print nozzle moves along a pre-set trajectory, while the molten raw material is quickly extruded and cooled, and stacked layer by layer to form. However, the strength, stiffness and heat resistance of parts produced using only thermoplastic materials are not high, which cannot meet production needs. Therefore, fiber particles are usually added in the fused deposition modeling process to improve the performance of thermoplastic materials. At the same time, the movement and distribution of fiber particles can also cause problems such as clogging of the print nozzle and reduced printing efficiency. Therefore, studying the movement characteristics of slender flexible particles in the fused deposition modeling process has an important guiding role in the improvement and optimization of fused deposition modeling equipment.

At present, many numerical simulation studies regard molten thermoplastic materials as Newtonian fluids. However, from the perspective of rheology, molten thermoplastic materials are non-Newtonian fluids with shear-thinning properties, which are manifested as viscosity decreasing with increasing shear rate. For slender flexible particles in molten thermoplastic materials, the shear-thinning property can significantly reduce the apparent viscosity around the particles, change the local flow field structure near the particles, and affect the orientation of slender flexible particles. However, existing computational fluid dynamics methods are difficult to achieve numerical simulation of the interaction between non-Newtonian fluids and moving particles, and cannot accurately calculate the deformation, position and posture of moving particles in non-Newtonian fluids, as well as the drag coefficient, lift coefficient and torque coefficient. Therefore, the present invention uses the non-Newtonian Carreau model to characterize the rheological properties of molten thermoplastic materials, and uses overlapping grid technology to achieve large-scale movement and deformation of particles in fluids, which can realize the study of the motion characteristics of slender flexible particles in non-Newtonian fluids.

Summary of the invention

In order to solve the above problems in the prior art, the present invention provides a numerical simulation method for the interaction characteristics between complex fluids and slender flexible particles. The non-Newtonian Carreau model is used to characterize the rheological properties of thermoplastic materials in a molten state based on the computational fluid dynamics method, and the overlapping grid technology is used to realize the large-scale movement of particles in the fluid. The numerical simulation of the interaction between non-Newtonian fluids and moving particles can be realized, the deformation, position and posture of slender flexible particles can be predicted, and the drag coefficient, lift coefficient and moment coefficient of the particles can be accurately calculated.

In order to achieve the above object, the main technical solutions adopted by the present invention include:

The numerical simulation method of the complex fluid-slender flexible particle interaction characteristics includes the following steps:

Step 1: Use modeling software to draw the slender flexible particles and fluid domain model, and use the meshing tool to divide the fluid domain and the surrounding of the particles into meshes;

Step 2: Use OpenFoam software to establish a basic physical model for the drawn grid: basic control equations, including continuity equation, momentum equation, fluid constitutive equation and overlapping grid control equation;

Step 3: Define the physical parameters and initial conditions of non-Newtonian fluids and slender flexible particles. The physical parameters mainly include: fluid density, viscosity, particle aspect ratio, particle stiffness, etc. The initial conditions mainly include: liquid flow rate, etc.;

Step 4: Define the boundary conditions of the import and export of the computational domain;

Step 5: Discretize the equations of step 2, close and solve them using the initial and boundary conditions defined in steps 3 and 4;

Step 6: Initialize the entire computational domain, set the time step and simulation end time, iterate the algebraic equations in the computational domain, and solve the pressure and velocity distribution in the computational domain. Calculate the deformation, position and posture of slender flexible particles with different stiffness in non-Newtonian fluids, as well as the drag coefficient, lift coefficient and torque coefficient of the slender particles until the simulation time ends, complete the numerical simulation of the motion characteristics of slender flexible particles in the fused deposition modeling process, and use the time step mechanism to save the calculation data;

Step 7: Post-process the calculation results.

In the above step 1, due to the use of overlapping grid technology, the fluid domain is divided into structured hexahedral grids separately, and the local area around the slender flexible particles is divided into structured hexahedral grids, and then the two sets of grids are merged together. There will be overlapping parts between the grids. After preprocessing such as digging holes, the grids inside the particles will be dug out and excluded from the calculation, and an interpolation relationship will be established in the remaining grid overlapping area. Finally, the interpolation method is used to enable the two sets of grids to exchange data in the overlapping area to achieve the overall calculation of the flow field.

In the above step 2, the molten thermoplastic material flows in an incompressible laminar flow. Considering the interaction between the fluid and the flexible particles, the basic control equation is as follows:

(1) Fluid control equation

The fluid phase satisfies the mass conservation and momentum conservation equations:

in:

u is the fluid velocity, m/s;

ρ is the fluid density, kg/m ³ ;

p is pressure, pa;

f is the source term caused by fluid-particle interaction;

τ is the viscous stress, pa, calculated by formula (3):

τ＝2μD (3)

in:

μ is the apparent viscosity of the fluid, pa·s, calculated by the constitutive equation of non-Newtonian fluid;

D is the strain rate tensor, calculated by formula (4):

(2) Constitutive equations of non-Newtonian fluids

The Carreau model is used to characterize the rheological properties of molten thermoplastic materials. It can well describe the change of the viscosity of the molten raw materials with the shear rate. Its constitutive equation is:

in:

_μ0 is the viscosity of the fluid at the shear rate, pa·s;

μ _∞ is the viscosity at infinite shear rate, pa·s;

λ is the relaxation time of non-Newtonian fluid, s;

n is the power law exponent.

For the convenience of research, a dimensionless number characterizing the shear thinning degree of Carreau fluid is defined:

Carreau number:

Viscosity ratio:

in:

d is the characteristic length of the slender particles, m.

(3) Overlapping grid control equations

Overlapping grid technology allows unconstrained relative displacement between multiple independent grids, and uses interpolation methods to exchange flow field information between grids. Using this feature of overlapping grids, unconstrained six-degree-of-freedom motion of objects and motion of multi-level objects can be achieved.

The key to the overlay grid technology is to establish domain connection information for inter-grid computing information transmission. The processing steps are:

Step 1: Search for hole elements and find out the node elements that do not participate in the calculation;

Step 2: Find appropriate interpolation contributing nodes for edge (boundary) nodes from another set of grids in the overlapping area;

Step 3: Solve the interpolation coefficient according to the positional relationship between the edge (boundary) nodes and the interpolation contribution nodes;

Step 4: Optimize the overlapping area to reduce the amount of calculation.

The interpolation is finally completed by weighted summing the flow field values of all contributing units and the corresponding interpolation coefficients (or weight coefficients):

in:

φ is the information of any flow field, such as velocity and pressure;

ω _i is the interpolation coefficient (weight coefficient) of the i-th contributing unit;

φ _i is the flow field information value of the i-th contributing unit;

φ _I is the value of the interpolation boundary cell;

In addition, all interpolation coefficients need to be dimensionless and meet the following conditions:

After completing the interpolation of all interpolation boundary cells in the flow field, the next step is to update the value of formula (8) in the entire computational flow field, which is mainly achieved by modifying the matrix of the linear algebraic equation group after the equation is discretized. After discretizing the control equation, we can obtain a linear algebraic equation group similar to the following:

[A]·x＝b (10)

in:

[A] is the matrix coefficient;

x is the unknown quantity;

b is the source term on the right side.

The advantage of this matrix modification method is that the values of the interpolation boundary cells can be affected by their adjacent cells, so there is no need for multiple additional iterations.

In step 3 above, the physical parameters and initial conditions of the non-Newtonian fluid and the slender flexible particles are set, including fluid velocity, density, viscosity, particle aspect ratio, particle stiffness, etc. At the same time, for the convenience of research, the following dimensionless numbers are defined:

Particle Reynolds number:

Particle spin number:

Particle aspect ratio:

in:

c is the length of the elongated particle, m;

a is the diameter of the elongated particles, m;

ω is the angular velocity of the ellipsoidal particle, rad/s.

In step 4 above, the boundary conditions of the inlet and outlet of the computational domain are as follows: the inlet is set as the velocity inlet; the outlet is set as the pressure outlet; the wall is set as the slip wall, and the slip velocity is the same as the inlet velocity; and the particle surface is set as no slip.

In the above step 5, the finite volume method is used to discretize the equation of step 2, the PISO algorithm is used to realize velocity-pressure coupling, and the Rhie-Chow flux interpolation and stress-velocity coupling algorithm are used to introduce the pressure smoothing term to make the calculation more stable.

In step 6 above, the entire computational domain is initialized, the time step and the simulation end time are set, the algebraic equations in the computational domain are iterated repeatedly, the pressure and velocity distribution in the computational domain are solved, the deformation, position and posture of the slender flexible particles, as well as the drag coefficient, lift coefficient and moment coefficient of the slender particles are calculated, and the calculation formula is as follows:

OK:

Lift coefficient:

Torque coefficient:

in:

F _d is the resistance, N;

F _l is lift, N;

M is the moment, N·m;

A is the frontal area of the elongated particles, m ² ;

The present invention provides a numerical simulation method for the interaction characteristics of complex fluids and elongated flexible particles. Based on the movement process of elongated flexible particles in a fused deposition molding process, a non-Newtonian Carreau model is used to characterize the rheological properties of thermoplastic materials in a molten state, and the viscosity of the molten raw materials can be well described as a function of shear rate. An overlapping grid technology is used to achieve large-scale movement of elongated flexible particles in a fluid, and the interaction between the non-Newtonian fluid and the elongated flexible particles is fully considered. The deformation, position and posture of the elongated flexible particles can be predicted, and the drag coefficient, lift coefficient and moment coefficient of the particles can be accurately calculated, thereby greatly reducing the calculation cost and improving the accuracy of the calculation.

The numerical simulation method of the interaction characteristics between complex fluid and slender flexible particles provided by the present invention can provide an effective solution for the improvement and optimization design of fused deposition modeling equipment. It also has important theoretical significance and guiding role in the processes involving non-Newtonian fluids and slender particles in the fields of chemical industry and energy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a numerical simulation process of the present invention;

FIG2 is a schematic diagram of the force on the elongated particles in the present invention;

FIG3 is a schematic diagram of velocity distribution around elongated particles in the present invention;

FIG4 is a qualitative display of the drag coefficient of the elongated particles in the present invention;

FIG5 is a qualitative display of the lift coefficient of the elongated particles in the present invention;

FIG. 6 is a qualitative display of the moment coefficient of the slender particles in the present invention.

Detailed ways

The present invention provides a numerical simulation method for complex fluid-slender flexible particle interaction characteristics. FIG1 is a schematic diagram of the simulation process of the method, which includes the following steps:

Step 1: Use modeling software to draw the slender flexible particles and fluid domain model, and use the meshing tool to divide the fluid domain and the surrounding of the particles into meshes;

Step 2: Use OpenFoam software to establish a basic physical model for the drawn grid: basic control equations, including continuity equation, momentum equation, fluid constitutive equation and overlapping grid control equation;

Step 3: Define the physical parameters and initial conditions of non-Newtonian fluids and slender flexible particles. The physical parameters mainly include: fluid density, viscosity, particle aspect ratio, particle stiffness, etc. The initial conditions mainly include: liquid flow rate, etc.;

Step 4: Define the boundary conditions of the import and export of the computational domain;

Step 5: Discretize the equations of step 2, close and solve them using the initial and boundary conditions defined in steps 3 and 4;

Step 6: Initialize the entire computational domain, set the time step and simulation end time, iterate the algebraic equations in the computational domain, and solve the pressure and velocity distribution in the computational domain. Calculate the deformation, position and posture of slender flexible particles with different stiffness in non-Newtonian fluids, as well as the drag coefficient, lift coefficient and torque coefficient of the slender particles until the simulation time ends, complete the numerical simulation of the motion characteristics of slender flexible particles in the fused deposition modeling process, and use the time step mechanism to save the calculation data;

Step 7: Post-process the calculation results.

In the above step 1, due to the use of overlapping grid technology, the fluid domain is divided into structured hexahedral grids separately, and then the local area around the slender flexible particles is divided into structured hexahedral grids. The two sets of grids are then merged together. There will be overlapping parts between the grids. After preprocessing processes such as digging holes, the grids inside the particles will be dug out and excluded from the calculation, and an interpolation relationship will be established in the remaining grid overlapping area. Finally, the interpolation method is used to enable the two sets of grids to exchange data in the overlapping area to achieve overall calculation of the flow field.

In the above step 2, the molten thermoplastic material flows in an incompressible laminar flow. Considering the interaction between the fluid and the flexible particles, the basic control equation is as follows:

(1) Fluid control equation

The fluid phase satisfies the mass conservation and momentum conservation equations:

in:

u is the fluid velocity, m/s;

ρ is the fluid density, kg/m ³ ;

p is pressure, pa;

f is the source term caused by fluid-particle interaction;

τ is the viscous stress, pa, calculated by formula (3):

τ＝2μD (3)

in:

μ is the apparent viscosity of the fluid, pa·s, calculated by the constitutive equation of non-Newtonian fluid;

D is the strain rate tensor, calculated by formula (4):

(2) Constitutive equations of non-Newtonian fluids

The Carreau model is used to characterize the rheological properties of molten thermoplastic materials. It can well describe the change of the viscosity of the molten raw materials with the shear rate. Its constitutive equation is:

in:

_μ0 is the viscosity of the fluid at the shear rate, pa·s;

μ _∞ is the viscosity at infinite shear rate, pa·s;

λ is the relaxation time of non-Newtonian fluid, s;

n is the power law exponent.

For the convenience of research, a dimensionless number characterizing the shear thinning degree of Carreau fluid is defined:

Carreau number:

Viscosity ratio:

in:

d is the characteristic length of the slender particles, m.

(3) Overlapping grid control equations

Overlapping grid technology allows unconstrained relative displacement between multiple independent grids, and uses interpolation methods to exchange flow field information between grids. Using this feature of overlapping grids, unconstrained six-degree-of-freedom motion of objects and motion of multi-level objects can be achieved.

The key to the overlay grid technology is to establish domain connection information for inter-grid computing information transmission. The processing steps are:

Step 1: Search for hole elements and find out the node elements that do not participate in the calculation;

Step 2: Find appropriate interpolation contributing nodes for edge (boundary) nodes from another set of grids in the overlapping area;

Step 3: Solve the interpolation coefficient according to the positional relationship between the edge (boundary) nodes and the interpolation contribution nodes;

Step 4: Optimize the overlapping area to reduce the amount of calculation.

The interpolation is finally completed by weighted summing the flow field values of all contributing units and the corresponding interpolation coefficients (or weight coefficients):

in:

φ is the information of any flow field, such as velocity and pressure;

ω _i is the interpolation coefficient (weight coefficient) of the i-th contributing unit;

φ _i is the flow field information value of the i-th contributing unit;

φ _I is the value of the interpolation boundary cell;

In addition, all interpolation coefficients need to be dimensionless and meet the following conditions:

After completing the interpolation of all interpolation boundary cells in the flow field, the next step is to update the value of formula (8) in the entire computational flow field, which is mainly achieved by modifying the matrix of the linear algebraic equation group after the equation is discretized. After discretizing the control equation, we can obtain a linear algebraic equation group similar to the following:

[A]·x＝b(10)

in:

[A] is the matrix coefficient;

x is the unknown quantity;

b is the source term on the right side.

The advantage of this matrix modification method is that the values of the interpolation boundary cells can be affected by their adjacent cells, so there is no need for multiple additional iterations.

In step 3 above, the physical parameters and initial conditions of the non-Newtonian fluid and the slender flexible particles are set, including fluid velocity, density, viscosity, particle aspect ratio, particle stiffness, etc. At the same time, for the convenience of research, the following dimensionless numbers are defined:

Particle Reynolds number:

Particle spin number:

Particle aspect ratio:

in:

c is the length of the elongated particle, m;

a is the diameter of the elongated particles, m;

ω is the angular velocity of the ellipsoidal particle, rad/s.

The physical parameters and initial conditions used in the present invention are shown in Table 1 below:

Table 1 Physical parameters and initial conditions

Ar Re Spa α β n Case number one 1.5 90 2 - - 1 Case 2 1.5 90 2 1 0 0.5

In step 4 above, the boundary conditions of the inlet and outlet of the computational domain are as follows: the inlet is set as the velocity inlet; the outlet is set as the pressure outlet; the wall is set as the slip wall, and the slip velocity is the same as the inlet velocity; and the particle surface is set as no slip.

In the above step 5, the finite volume method is used to discretize the equation of step 2, the PISO algorithm is used to realize velocity-pressure coupling, and the Rhie-Chow flux interpolation and stress-velocity coupling algorithm are used to introduce the pressure smoothing term to make the calculation more stable.

In the above step 6, the entire computational domain is initialized, the time step and the simulation end time are set, the algebraic equations in the computational domain are iterated repeatedly, the pressure and velocity distribution in the computational domain are solved, the deformation, position and posture of the slender flexible particles, as well as the drag coefficient, lift coefficient and moment coefficient of the slender particles are calculated. Figure 2 is a schematic diagram of the force on the slender particles, and the calculation formula is as follows:

OK:

Lift coefficient:

Torque coefficient:

in:

F _d is the resistance, N;

F _l is lift, N;

M is the moment, N·m;

A is the frontal area of the elongated particles, m ² ;

The above numerical simulation scheme is solved and then the numerical results are analyzed.

Figure 3 shows the shape of the slender particles and the surrounding velocity distribution. It can be seen that the slender particles in the Carreau fluid will bend and deform under the action of the non-Newtonian fluid.

Figures 4, 5 and 6 show the relationship between the drag coefficient, lift coefficient and moment coefficient of the slender particles and the rotation inclination angle of the slender particles in Scheme 1 and Scheme 2, respectively. In Scheme 1, the n value of the Carreau model is 1, and the fluid is a Newtonian fluid. It can be seen that the curves of the drag coefficient Cd, lift coefficient Cl and moment coefficient Cm of the particles in Scheme 1 are in good agreement with the data in the literature, proving the accuracy of the calculation of this numerical scheme. Scheme 2 is a pseudoplastic fluid. It can be seen that at the same particle rotation inclination angle α, the drag coefficient and moment coefficient of the particles in the pseudoplastic fluid are both smaller than those of the Newtonian fluid, mainly because the shear rate of the fluid around the particles is large, and the viscosity of the pseudoplastic fluid decreases with the increase of the shear rate. The decrease in viscosity will cause the viscous stress on the sphere to decrease. The lift coefficient value is greater than that of the Newtonian fluid, and a positive value will appear.

In summary, the numerical simulation method of the complex fluid-slender flexible particle interaction characteristics proposed in the present invention can predict the deformation, position and posture of the slender flexible particles, and accurately calculate the drag coefficient, lift coefficient and moment coefficient of the particles.

The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any person skilled in the art can use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims (5)

1. A method for numerically modeling complex fluid-elongated flexible particle interaction characteristics, comprising the steps of:

Step 1: drawing an elongated flexible particle and a fluid domain model by using modeling software, and meshing the fluid domain and the periphery of the particle by using a meshing tool;

The method comprises the steps of (1) independently dividing a fluid domain into structured hexahedral meshes by using an overlapped mesh technology, dividing a local area around an elongated flexible particle into the structured hexahedral meshes, and merging two sets of meshes together; the grids have overlapping parts, after the pretreatment process, the grids in the particles can be excavated and excluded from calculation, interpolation relation is built in the overlapping areas of the remaining grids, and finally data exchange can be carried out between the two sets of grids in the overlapping areas through an interpolation method, so that the overall calculation of a flow field domain is achieved;

Step 2: a basic physical model is built for the drawn mesh using OpenFoam software: basic control equations, including continuity equations, momentum equations, fluid constitutive equations, and overlapping grid control equations;

the thermoplastic material in the molten state is an incompressible laminar flow, whose basic control equation is as follows, taking into account the interaction between the fluid and the flexible particles:

(1) Equation of fluid control

The fluid phase satisfies the mass conservation and momentum conservation equations:

wherein:

u is the fluid velocity, m/s;

ρ is the fluid density, kg/m ³;

p is pressure, pa;

f is the source term caused by the fluid-particle interactions;

τ is the viscous stress, pa, calculated from equation (3):

τ＝2μD(3)

wherein:

mu is the apparent viscosity of the fluid, pa.s, calculated from the constitutive equation of a non-Newtonian fluid;

d is the strain rate tensor, calculated from equation (4):

(2) Constitutive equation for non-Newtonian fluids

The rheological properties of a thermoplastic material in the molten state are characterized using a Carreau model, describing the viscosity of the molten raw material as a function of shear rate, whose constitutive equation is:

wherein:

mu ₀ is the viscosity at zero shear rate of the fluid, pa.s;

Mu _∞ is the viscosity at infinite shear rate, pa.s;

lambda is the relaxation time of the non-newtonian fluid, s;

n is a power law exponent;

defining a dimensionless number characterizing the degree of shear thinning of the Carreau fluid:

Carreau number:

Viscosity ratio:

wherein:

d is the characteristic length of the elongated particles, m;

(3) Overlapped grid control equation

The overlapped grid technology allows unconstrained relative displacement to be generated among a plurality of grids which are independent of each other, and flow field information among the grids can be exchanged by utilizing an interpolation method; by utilizing the characteristic of the overlapped grid, the unconstrained six-degree-of-freedom motion of the object and the motion of the multi-stage object are realized;

The key of the overlapped grid technology is to establish domain connection information for the transmission of calculation information among grids, and the processing steps are as follows:

Step 1: searching a hole unit, and finding out node units which do not participate in calculation;

step 2: searching a proper interpolation contribution node from another set of grids of the overlapping area for the edge node;

Step 3: solving interpolation coefficients according to the position relation between the edge nodes and the interpolation contribution nodes;

step 4: the overlapping area is optimized, and the calculated amount is reduced;

the interpolation is finally completed by weighted summation of the flow field values of all the contribution units and the corresponding interpolation coefficients or weighting coefficients:

wherein:

Phi is information of any flow field, such as speed or pressure;

Omega _i is the interpolation coefficient of the ith contribution unit;

phi _i is the flow field information value of the ith contribution unit;

phi _I is the value of the interpolation boundary unit;

furthermore, all interpolation coefficients need to be dimensionless and meet the following conditions:

After interpolation of all interpolation boundary units in the flow field is completed, updating the value of the formula (8) in the whole calculation flow field, and modifying a linear algebraic equation set matrix after equation dispersion to realize the calculation flow field; after discretizing the control equation, the following set of linear algebraic equations is obtained:

[A]·x＝b(10)

wherein:

[A] Is a matrix coefficient;

x is an unknown quantity;

b is a right-end source item;

Step 3: defining physical properties parameters and initial conditions of the non-Newtonian fluid and the elongated flexible particles, wherein the physical properties parameters include: fluid density, viscosity, particle aspect ratio, and particle stiffness, initial conditions include: a liquid flow rate;

step 4: defining boundary conditions of the import and export of the calculation domain;

step 5: discretizing the equation in the step 2, and sealing and solving by adopting the initial conditions and the boundary conditions defined in the step 3 and the step 4;

step 6: initializing the whole calculation domain, setting a time step length and a simulation ending time length, repeatedly iterating an algebraic equation set in the calculation domain, and solving the pressure and speed distribution in the calculation domain; calculating deformation, positions and postures of the elongated flexible particles with different rigidities in the non-Newtonian fluid, and resistance coefficients, lift coefficients and moment coefficients of the elongated particles until the simulation time is over, completing numerical simulation of the motion characteristics of the elongated flexible particles in the fused deposition modeling process, and storing calculation data by utilizing a time step mechanism;

step 7: and carrying out post-processing on the calculation result.

2. A method of numerical modeling of complex fluid-elongated flexible particle interaction characteristics as claimed in claim 1 wherein: in the step 3, physical parameters and initial conditions of the non-Newtonian fluid and the elongated particles are set, including fluid speed, density, viscosity, particle aspect ratio and particle rigidity; at the same time, the following dimensionless numbers are defined:

particle reynolds number:

particle spin number:

Aspect ratio of particles:

wherein:

c is the length of the elongated particles, m;

a is the diameter of the elongated particles, m;

omega is the rotation angular velocity of the elongated particles, rad/s.

3. A method of numerical modeling of complex fluid-elongated flexible particle interaction characteristics as claimed in claim 1 wherein: in the step 4, calculating boundary conditions of the domain import and export: the inlet is set as a speed inlet; the outlet is set as a pressure outlet; the wall surface is set as a sliding wall surface, and the sliding speed is the same as the inlet speed; the surface of the elongated particles is arranged to be slip-free.

4. A method of numerical modeling of complex fluid-elongated flexible particle interaction characteristics as claimed in claim 1 wherein: in the step 5, the equation of the step 2 is discretized by adopting a finite volume method, the PISO algorithm is used for realizing the speed-pressure coupling, and the Rhie-Chow flux interpolation and the stress-speed coupling algorithm are used for introducing a pressure smoothing term.

5. A method of numerical modeling of complex fluid-elongated flexible particle interaction characteristics as claimed in claim 1 wherein: in the step6, initializing the whole calculation domain, setting a time step and a simulation ending time length, repeatedly iterating algebraic equations in the calculation domain, solving pressure and speed distribution in the calculation domain, calculating deformation, position and posture of the elongated flexible particles, and resistance coefficients, lift coefficients and moment coefficients of the elongated particles, wherein a calculation formula is as follows:

Coefficient of resistance:

Lift coefficient:

Moment coefficient:

wherein:

F _d is resistance, N;

F _l is lift force, N;

m is moment, N.m;

A is the windward area of the elongated particles, m ².