CN117875140B - Numerical simulation method for complex fluid-slender flexible particle interaction characteristics - Google Patents
Numerical simulation method for complex fluid-slender flexible particle interaction characteristics Download PDFInfo
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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
Technical Field
The invention relates to a numerical simulation method for complex fluid-slender flexible particle interaction characteristics, and belongs to the technical field of method inventions.
Background
Additive manufacturing technology, also known as 3D printing, is a technology that utilizes a bondable material such as powdered metal or plastic to construct an object by way of layer-by-layer printing. Fused deposition modeling is the most mature and simplest 3D printing technology currently developed. The working principle of the technology is that thermoplastic materials are heated to a molten state in a spray head, the printing spray head moves along a preset track, and meanwhile, raw materials in the molten state are rapidly extruded and cooled, and are stacked layer by layer to be formed. However, the strength, rigidity and heat resistance of parts produced by using only thermoplastic materials are not high, and the production requirements cannot be met. Accordingly, fiber particles are typically added during fused deposition modeling to enhance the properties of the thermoplastic material. At the same time, the movement and distribution of the fiber particles also cause problems such as blockage of the printing nozzle, reduced printing efficiency, and the like. Thus, studying the motion characteristics of elongated flexible particles in fused deposition modeling processes has an important guiding role in the improvement and optimization of fused deposition modeling equipment.
Currently, many numerical modeling studies consider thermoplastic materials in the molten state as newtonian fluids. From a rheological standpoint, however, the thermoplastic material in the molten state is a non-newtonian fluid with shear thinning characteristics that manifest as a decrease in viscosity with increasing shear rate. For elongated flexible particles in a thermoplastic material in a molten state, the shear thinning characteristics can significantly reduce the apparent viscosity around the particles, altering the local flow field structure near the particles, affecting the orientation of the elongated flexible particles. However, the existing computational fluid dynamics method is difficult to realize numerical simulation of interaction between the non-newtonian fluid and the moving particles, and deformation, position and posture of the moving particles in the non-newtonian fluid, as well as drag coefficient, lift coefficient and moment coefficient cannot be accurately calculated. Therefore, the invention uses a non-Newtonian Carreau model to characterize the rheological property of the thermoplastic material in a molten state, and uses an overlapped grid technology to realize the large-amplitude movement and deformation of particles in the fluid, so that the research on the movement characteristics of the slender flexible particles in the non-Newtonian fluid can be realized.
Disclosure of Invention
In order to solve the problems of the prior art, the invention provides a numerical simulation method for complex fluid-slender flexible particle interaction characteristics, a non-Newtonian Carreau model is used for representing rheological properties of a thermoplastic material in a molten state based on a computational fluid mechanics method, large-amplitude movement of particles in a fluid is realized by using an overlapped grid technology, numerical simulation of interaction between the non-Newtonian fluid and moving particles can be realized, deformation, position and posture of the slender flexible particles can be predicted, and resistance coefficients, lift coefficients and moment coefficients of the particles can be accurately calculated.
In order to achieve the above purpose, the main technical scheme adopted by the invention comprises the following steps:
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;
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;
Step 3: defining physical properties parameters and initial conditions of the non-Newtonian fluid and the elongated flexible particles, wherein the physical properties parameters mainly comprise: fluid density, viscosity, particle aspect ratio, particle stiffness, etc., the initial conditions mainly include: liquid flow rate, etc.;
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 the 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.
In step 1, the fluid domain is divided into the structured hexahedral mesh by itself, the local area around the elongated flexible particles is divided into the structured hexahedral mesh by using the overlapping mesh technique, and the two meshes are combined together. And overlapping parts exist between grids, the grids in the particles are excavated and excluded from calculation after pretreatment processes such as hole excavation and the like, interpolation relations are 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.
In step 2 above, the thermoplastic material in the molten state is in an incompressible laminar flow, the basic control equation taking into account the interaction between the fluid and the flexible particles is as follows:
(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 property of the thermoplastic material in the molten state is represented by using a Carreau model, so that the change condition of the viscosity of the molten raw material along with the shear rate can be well described, and the constitutive equation is as follows:
wherein:
Mu 0 is the viscosity at the shear rate of the fluid regime, 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.
For ease of investigation, a dimensionless number is defined that characterizes the degree of shear thinning of the Carreau fluid:
Carreau number:
Viscosity ratio:
wherein:
d is the characteristic length of the elongated particle, m.
(3) Overlapped grid control equation
The overlapping grid technique may allow unconstrained relative displacement between multiple mutually independent grids and allow for exchange of flow field information between the grids using interpolation methods. By utilizing the characteristic of the overlapped grid, the object can realize unconstrained six-degree-of-freedom motion and multi-stage object motion.
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 for a suitable interpolation contribution node from another set of grids of the overlapping region for an edge (boundary) node;
Step 3: solving interpolation coefficients according to the position relation between edge (boundary) nodes and interpolation contribution nodes;
step 4: and 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 called weighting coefficients):
wherein:
Phi is information of any flow field, such as speed, pressure and the like;
Omega i is the interpolation coefficient (weight coefficient) of the i-th 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, the value of the formula (8) needs to be updated in the whole calculation flow field in the next step, and the method is mainly realized by modifying a linear algebraic equation set matrix after equation dispersion. After discretizing the control equation, we can get a system of linear algebraic equations like the following:
[A]·x＝b (10)
wherein:
[A] Is a matrix coefficient;
x is an unknown quantity;
b is the right-end source item.
The advantage of this approach by modifying the matrix is that the value of the interpolated boundary cell can be influenced to its neighboring cells, thus eliminating the need for multiple additional iterations.
In step 3 above, physical parameters and initial conditions of the non-newtonian fluid and the elongated flexible particles are set, including fluid velocity, density, viscosity, particle aspect ratio, particle stiffness, etc. Meanwhile, for convenience of study, 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 rotational angular velocity of the ellipsoidal particles and rad/s.
In the step 4, the boundary condition of the domain import and export is calculated: 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 particle surface is set to be slip-free.
In the step 5, the equation in 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, so that the calculation is more stable.
In the step 6, 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 slender particles, m 2;
the invention provides a numerical simulation method for complex fluid-slender flexible particle interaction characteristics, which is based on the movement process of the slender flexible particles in the fused deposition modeling 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 a 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 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, accurately calculates the resistance coefficient, the lift coefficient and the moment coefficient of the particles, greatly reduces the calculation cost and improves the calculation accuracy.
The numerical simulation method for the interaction characteristics of the complex fluid and the slender flexible particles can provide an effective solution for the improvement and the optimization design of fused deposition modeling equipment, and has important theoretical significance and guidance on the processes involving non-Newtonian fluid and slender particles in the fields of chemical industry, energy sources and the like.
Drawings
FIG. 1 is a schematic diagram of a numerical simulation flow chart of the present invention;
FIG. 2 is a schematic diagram of the force exerted on an elongated particle in accordance with the present invention;
FIG. 3 is a schematic representation of the velocity distribution around an elongated particle in the present invention;
FIG. 4 is a qualitative representation of the drag coefficient of elongated particles in the present invention;
FIG. 5 is a qualitative representation of the lift coefficient of an elongated particle in the present invention;
fig. 6 is a qualitative representation of moment coefficients of elongated particles in accordance with the present invention.
Detailed Description
The invention provides a numerical simulation method of complex fluid-slender flexible particle interaction characteristics, and fig. 1 is a schematic diagram of a simulation flow of the method, and the method comprises the following steps:
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;
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;
Step 3: defining physical properties parameters and initial conditions of the non-Newtonian fluid and the elongated flexible particles, wherein the physical properties parameters mainly comprise: fluid density, viscosity, particle aspect ratio, particle stiffness, etc., the initial conditions mainly include: liquid flow rate, etc.;
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 the 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.
In the step 1, the fluid domain is divided into the structured hexahedral meshes by using the overlapped mesh technology, the local area around the elongated flexible particles is divided into the structured hexahedral meshes, the two sets of meshes are combined together, an overlapped part exists between the meshes, the meshes in the particles are excavated and excluded from calculation after the pretreatment process such as hole excavation, and an interpolation relation is established in the overlapped area of the residual meshes, and finally, data exchange can be performed between the two sets of meshes in the overlapped area by using the interpolation method, so that the integral calculation of the flow field domain is achieved.
In step 2 above, the thermoplastic material in the molten state is in an incompressible laminar flow, the basic control equation taking into account the interaction between the fluid and the flexible particles is as follows:
(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 property of the thermoplastic material in the molten state is represented by using a Carreau model, so that the change condition of the viscosity of the molten raw material along with the shear rate can be well described, and the constitutive equation is as follows:
wherein:
Mu 0 is the viscosity at the shear rate of the fluid regime, 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.
For ease of investigation, a dimensionless number is defined that characterizes the degree of shear thinning of the Carreau fluid:
Carreau number:
Viscosity ratio:
wherein:
d is the characteristic length of the elongated particle, m.
(3) Overlapped grid control equation
The overlapping grid technique may allow unconstrained relative displacement between multiple mutually independent grids and allow for exchange of flow field information between the grids using interpolation methods. By utilizing the characteristic of the overlapped grid, the object can realize unconstrained six-degree-of-freedom motion and multi-stage object motion.
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 for a suitable interpolation contribution node from another set of grids of the overlapping region for an edge (boundary) node;
Step 3: solving interpolation coefficients according to the position relation between edge (boundary) nodes and interpolation contribution nodes;
step 4: and 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 called weighting coefficients):
wherein:
Phi is information of any flow field, such as speed, pressure and the like;
Omega i is the interpolation coefficient (weight coefficient) of the i-th 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, the value of the formula (8) needs to be updated in the whole calculation flow field in the next step, and the method is mainly realized by modifying a linear algebraic equation set matrix after equation dispersion. After discretizing the control equation, we can get a system of linear algebraic equations like the following:
[A]·x＝b(10)
wherein:
[A] Is a matrix coefficient;
x is an unknown quantity;
b is the right-end source item.
The advantage of this approach by modifying the matrix is that the value of the interpolated boundary cell can be influenced to its neighboring cells, thus eliminating the need for multiple additional iterations.
In step 3 above, physical parameters and initial conditions of the non-newtonian fluid and the elongated flexible particles are set, including fluid velocity, density, viscosity, particle aspect ratio, particle stiffness, etc. Meanwhile, for convenience of study, 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 rotational angular velocity of the ellipsoidal particles and rad/s.
The physical properties and initial conditions used in the present invention are shown in table 1 below:
TABLE 1 physical Property parameters and initial conditions
| Ar | Re | Spa | α | β | n | |
| Case one | 1.5 | 90 | 2 | - | - | 1 |
| Case two | 1.5 | 90 | 2 | 1 | 0 | 0.5 |
In the step 4, the boundary condition of the domain import and export is calculated: 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 particle surface is set to be slip-free.
In the step 5, the equation in 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, so that the calculation is more stable.
In the step 6, the whole calculation domain is initialized, the time step and the simulation ending time are set, the algebraic equation set in the calculation domain is iterated repeatedly, the pressure and speed distribution in the calculation domain is solved, the deformation, the position and the posture of the elongated flexible particles, the resistance coefficient, the lift coefficient and the moment coefficient of the elongated particles are calculated, fig. 2 is a stress schematic diagram of the elongated particles, and the 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 slender particles, m 2;
and solving the numerical simulation scheme, and then analyzing the numerical result.
Fig. 3 shows the shape and surrounding velocity profile of the elongated particles, and it can be seen that the elongated particles in the Carreau-type fluid are subject to bending deformation by the non-newtonian fluid.
Fig. 4, 5 and 6 show the relationship between the drag coefficient, lift coefficient and moment coefficient of the elongated particle and the rotation inclination angle of the elongated particle in the first and second embodiments, respectively. The n value of the Carreau model in the scheme I is 1, the fluid is Newtonian fluid, and it can be seen that the curves of the resistance coefficient Cd, the lift coefficient Cl and the moment coefficient Cm of the particles in the scheme I are well matched with the data in the literature, so that the calculation accuracy of the numerical scheme is proved. In the second scheme, the resistance coefficient and the moment coefficient of the particles in the pseudoplastic fluid are smaller than those of the newtonian fluid under the same rotation inclination angle alpha of the particles, mainly because the shear rate of the fluid around the particles is larger, the viscosity of the pseudoplastic fluid is reduced along with the increase of the shear rate, and the viscosity reduction can lead to the reduction of the viscous stress born by the sphere. Whereas the value of the lift coefficient is greater than newtonian and positive values occur.
In summary, the numerical simulation method for complex fluid-elongated flexible particle interaction characteristics provided by the invention can predict deformation, position and posture of the elongated flexible particles and accurately calculate the resistance coefficient, lift coefficient and moment coefficient of the particles.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any person skilled in the art may make modifications or alterations to the above disclosed technical content to equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within 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.
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