CN113051842A - non-Newtonian fluid simulation method and device - Google Patents
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Abstract
The invention provides a non-Newtonian fluid simulation method and a non-Newtonian fluid simulation device, wherein the method comprises the following steps: respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation; coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspended body model with the property between the liquid phase and the suspended particle phase; constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model; and constructing a friction function according to the particle skeletal structure change of the two-phase suspension model, and adding the friction function into the elastic-plastic constitutive model for simulating the rheological property of the non-Newtonian fluid. The invention realizes the simulation of non-Newtonian property by modeling the real physical mechanism of the bottom layer, provides physical interpretable parameter control, thereby uniformly simulating different types of non-Newtonian fluids and accurately depicting the rheological property of the non-Newtonian fluids.
Description
Technical Field
The invention relates to the technical field of computer graphics fluid simulation and rendering, in particular to a non-Newtonian fluid simulation method and device.
Background
Non-newtonian fluids differ from general fluids in that their viscosity changes with shear flow and are widely used in everyday life and industrial applications, such as ketchup, cream and various lubricants. Non-newtonian fluids are also gaining increasing attention in the graphics arts due to their wide use and display of rich visual effects. The complex rheological properties of non-newtonian fluids are not fully understood compared to general newtonian fluids, and their highly nonlinear behavior also presents significant challenges to simulation.
It is now common practice in the industry to describe non-newtonian fluids using an exponential model, for example, the Herschel-Bulkley model,
wherein τ is shear stress, τ0The yield stress, k is the consistency index and n is the fluidity index. When n is more than 1, the fluid is shear thickening fluid; when n is<1, shear-thinning fluid. Based on this unique image description, there have been many efforts in graphics to successfully simulate various non-Newtonian fluids, such as, for example, the method of codimensional simulation proposed by Zhu et al, which can simulate a non-Newtonian fluid that is spread into a thin layer, and the method of simulating substances such as shaving foam that have a viscosity that varies with shear rate proposed by Yue et al.
However, these prior art methods treat non-newtonian fluids as homogeneous single fluids, ignoring the internal microstructure. However, most non-Newtonian fluids are suspensions, i.e., a complex system of small particles suspended in Newtonian fluids, such as various sauces, creams, blood, etc., are suspensions that do not truly mimic the properties of non-Newtonian fluids. Therefore, there is a need for a non-Newtonian fluid simulation method and apparatus to solve the above problems.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a non-Newtonian fluid simulation method and a non-Newtonian fluid simulation device.
The invention provides a non-Newtonian fluid simulation method, which comprises the following steps:
respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation;
coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase;
constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model;
and constructing a friction function according to the particle skeletal structure change of the two-phase suspension model, and adding the friction function into the elastic-plastic constitutive model for simulating the rheological property of the non-Newtonian fluid.
According to the non-Newtonian fluid simulation method provided by the invention, the fluid resistance formula is as follows:
wherein k isdDenotes the resistance constant, usDenotes the suspended particle phase velocity ufDenotes the liquid phase velocity, d denotes the suspended particle diameter, eta denotes the fluid viscosity, phisRepresents the suspended particle phase volume fraction;
the fluid pressure equation is:
wherein p isfDenotes the liquid phase density, pf0Denotes the liquid phase static density and κ denotes the stiffness coefficient.
According to the non-Newtonian fluid simulation method provided by the invention, the elastic-plastic constitutive model based on the suspended particle phase is constructed according to the plastic shear stress and the volume change of the two-phase suspension model, and the method comprises the following steps:
from the plastic shear stress, a first yield condition is established:
τ≤(μ+β)p；
wherein τ represents shear stress, μ represents friction coefficient, IvDenotes the viscosity number, phimRepresents the maximum suspended particle phase volume fraction, beta represents the expansion angle, p represents the pressure,
representing the plastic shear rate, eta the liquid viscosity coefficient, mu1Denotes the viscosity number IvCoefficient of friction, mu, to 02Denotes the viscosity number IvCoefficient of friction to ∞, I0Is a constant parameter;
from the plastic stretching, a second yield condition is established:
p+∈≥0；
wherein epsilon represents a preset viscosity threshold value;
from the plastic compression, a third yield condition is established:
wherein φ represents the suspended particle phase volume fraction, and g (φ) represents a coefficient that varies with φ;
and constructing and obtaining an elastic-plastic constitutive model based on the suspended particle phase according to the yield surfaces corresponding to the first yield condition, the second yield condition and the third yield condition respectively.
According to the non-Newtonian fluid simulation method provided by the invention, the formula of the friction function is as follows:
φm＝φj+(φc-φj)Ψ；
wherein the content of the first and second substances,
representing the friction function of the particle after a change in the skeletal structure, cfA constant indicating a control change rate, H indicates a hardening rate,
representing the plastic shear rate, ΨmRepresenting the maximum value of the friction function, psi representing the friction function before the change of the particle skeleton structure, xi representing the buckling coefficient, tau representing the shear stress, tau*Denotes the repulsion constant between particles, cbAnd l is a constant, phi, controlling the buckling effectmDenotes the maximum suspended particle phase volume fraction, phi denotes the suspended particle phase volume fraction, phicIs indicative of phimLower bound of (phi)jIs indicative of phimThe upper bound of (c).
According to the invention, the non-Newtonian fluid simulation method further comprises the following steps:
and carrying out discrete simulation solution on the elastic-plastic constitutive model by a material point method to obtain the rheological property of the non-Newtonian fluid.
According to the non-newtonian fluid simulation method provided by the invention, the elastic-plastic constitutive model is solved through discrete simulation by a material point method, and the method further comprises the following steps:
simulating the permeation between the liquid and the dry particles based on a liquid drift velocity model, the liquid drift velocity model being:
wherein, cdDenotes the diffusion constant,. phifIndicating the liquid phase volume fraction.
According to the non-Newtonian fluid simulation method provided by the invention, the liquid phase and the suspended particle phase of the non-Newtonian fluid are respectively simulated based on the continuity equation and the momentum equation, and the method comprises the following steps:
simulating a suspended particle phase in the non-Newtonian fluid based on a solid continuity equation and a solid momentum equation, the solid continuity equation being:
the solid momentum equation is as follows:
wherein the content of the first and second substances,
represents the solid-phase equivalent density, ρsDenotes the solid phase density, t denotes the time, usRepresenting the suspended particle phase velocity, g representing gravity, fdRepresenting the fluid resistance, σsDenotes shear stress,. phisRepresents the solid phase volume fraction;
simulating a liquid phase in the non-Newtonian fluid based on a liquid continuity equation and a liquid momentum equation, wherein the liquid continuity equation is as follows:
the liquid momentum equation is as follows:
wherein phi isfRepresenting the liquid phase volume fraction, pfDenotes the liquid phase density, ufWhich is indicative of the velocity of the liquid phase,
denotes the liquid phase equivalent density, σfIndicating viscous stress.
The present invention also provides a non-Newtonian fluid simulation device, comprising:
the first simulation module is used for respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation;
the coupling module is used for coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase;
the model construction module is used for constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model;
and the second simulation module is used for constructing a friction function according to the particle skeletal structure change of the two-phase suspension model and adding the friction function into the elastic-plastic constitutive model so as to simulate the rheological property of the non-Newtonian fluid.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the steps of any one of the above-described non-newtonian fluid simulation methods.
The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the non-newtonian fluid simulation method as described in any one of the above.
The non-Newtonian fluid simulation method and device provided by the invention provide a non-Newtonian fluid simulation method with higher expansibility, realize the simulation of non-Newtonian properties by modeling the real physical mechanism of the bottom layer of the non-Newtonian fluid simulation method, and provide parameter control which can be interpreted physically, thereby uniformly simulating different types of non-Newtonian fluids and accurately describing the rheological property of the non-Newtonian fluids.
Drawings
In order to more clearly illustrate the technical solutions of the present invention or the prior art, the drawings needed for the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a non-Newtonian fluid simulation method provided by the present invention;
FIG. 2 is a schematic illustration of a yielding surface provided by the present invention;
FIG. 3 is a schematic representation of three shear thickening rheology mechanisms provided by the present invention;
FIG. 4 is a schematic diagram of a non-Newtonian fluid simulation device in accordance with the present invention;
fig. 5 is a schematic structural diagram of an electronic device provided in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Although most non-Newtonian fluids belong to suspension, the existing simulation method for non-Newtonian fluids ignores the internal microstructure and treats the non-Newtonian fluids as a uniform single fluid, so that the simulation results in that the non-Newtonian fluids can not completely describe the real characteristics. Based on the above, the invention uses two phases to simulate the non-Newtonian fluid, can simulate the non-uniform non-Newtonian fluid, and can even directly start from raw materials (namely water and powder) to simulate the formation of the non-Newtonian fluid, thereby greatly expanding the phenomenon which can be simulated. Particularly for a discontinuous type of shear thickening phenomenon, in materials such as the European Union Jack (ovleck), which may exhibit rigid-like properties when sheared, but may return to fluid when left undisturbed, this is closely related to the structural changes within.
Fig. 1 is a schematic flow chart of a non-newtonian fluid simulation method provided by the present invention, and as shown in fig. 1, the present invention provides a non-newtonian fluid simulation method, including:
According to the method, a liquid phase and a suspended particle phase of the non-Newtonian fluid are obtained through simulation by taking two independent continuous medium phases as targets through a continuity equation and a momentum equation corresponding to liquid and suspended particles in the non-Newtonian fluid, wherein the suspended particle phase is a micro particle suspended in the non-Newtonian fluid and is described through the continuity equation and the momentum equation. Specifically, continuity equations are used to update particle density, while kinetic equations, including gravity, viscous forces, pressure, and shear stress, are used to update particle velocity.
And 102, coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase.
In the invention, fluid resistance and fluid pressure are applied to the two phases to generate the effect of solid-liquid strong coupling, and the property between the solid and the liquid is displayed, so that a two-phase suspension model of the property between the liquid phase and the suspended particle phase is obtained.
And 103, constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model.
According to the method, 3 plastic yield conditions are designed according to the characteristics of the two-phase suspension model, so that the elastoplasticity constitutive model based on the suspended particle phase is constructed and obtained.
And 104, constructing a friction function according to the particle skeletal structure change of the two-phase suspension model, and adding the friction function into the elastoplasticity constitutive model to simulate the rheological property of the non-Newtonian fluid.
In the invention, when a liquid phase and a suspended particle phase of a non-Newtonian fluid are respectively simulated, firstly, model parameters suitable for a target non-Newtonian fluid are preset, wherein the model parameters comprise yield condition parameters, updating parameters of a friction function, suspended particle diameter, liquid viscosity coefficient and the like, and the friction function is used for describing the change of a microscopic particle bone structure in a shear flow, so that the phenomenon of discontinuous shear thickening is simulated; further, the invention adopts a material point method, the material to be simulated (namely a liquid phase and a suspended particle phase) is converted into discrete material point particles, fluid resistance and fluid pressure are applied to the two phases, the effect of solid-liquid strong coupling is generated, each particle has proper density, mass and volume fraction, and a grid with proper size and resolution is generated for a simulation area for the calculation of the material point method; then, calculating respective volume fractions of two phases at any position in space through an elastic-plastic constitutive model; after the stress tensor of the suspended particles is updated, projecting the updated stress tensor of the suspended particle phase particles to yield surfaces corresponding to 3 yield conditions in an elastic-plastic constitutive model, so as to generate the characteristics of the non-Newtonian fluid and simulate the motion of the non-Newtonian fluid; finally, the invention draws each time step information obtained in the simulation on a display terminal to obtain a simulation image of the non-Newtonian fluid, and the simulation image is exported to be a data file for subsequent processing.
The non-Newtonian fluid simulation method provided by the invention provides a non-Newtonian fluid simulation method with higher expansibility, the simulation of non-Newtonian properties is realized by modeling a real physical mechanism of the bottom layer of the non-Newtonian fluid simulation method, and parameter control which can be interpreted physically is provided, so that different types of non-Newtonian fluids are simulated uniformly, and the rheological property of the non-Newtonian fluid is accurately described.
On the basis of the above embodiment, the fluid resistance formula is:
wherein k isdDenotes the resistance constant, usDenotes the suspended particle phase velocity ufDenotes the liquid phase velocity, d denotes the suspended particle diameter, eta denotes the fluid viscosity, phisRepresents the suspended particle phase volume fraction;
the fluid pressure equation is:
wherein p isfDenotes the liquid phase density, pf0Denotes the liquid phase static density and κ denotes the stiffness coefficient.
In the present invention, the two phases obtained by simulation of the above embodiments are coupled by fluid resistance and fluid pressure, and in the fluid resistance formula, the resistance is proportional to the velocity difference of the two phases and inversely proportional to the square of the suspended particle diameter. In the case of small suspended particles, the resistance becomes very large, and the present invention calculates it by using the reverse euler method. The present invention couples two phases via resistance and pressure to simulate the complex rheology of non-newtonian fluids between fluids and solids.
On the basis of the above embodiment, the constructing an elastoplastic constitutive model based on suspended particle phases according to the plastic shear stress and the volume change of the two-phase suspension model includes:
from the plastic shear stress, a first yield condition is established:
τ≤(μ+β)p；
wherein τ represents shear stress; μ denotes the coefficient of friction, IvRepresenting viscosity number, coefficient of friction with viscosity number Iv(ii) a change; phi is amRepresents the maximum suspended particle phase volume fraction; beta represents the expansion angle, beta ═ ca(φ-φeq)，caIs a constant number of times, and is,
is the equilibrium volume fraction; p represents the pressure of the gas to be pressurized,
representing the plastic shear rate, eta the liquid viscosity coefficient, mu1Denotes the viscosity number IvCoefficient of friction, mu, to 02Denotes the viscosity number IvCoefficient of friction to ∞, I0Is a constant parameter;
from the plastic stretching, a second yield condition is established:
p+∈≥0；
wherein epsilon represents a preset viscosity threshold value;
from the plastic compression, a third yield condition is established:
wherein φ represents the suspended particle phase volume fraction, and g (φ) represents a coefficient that varies with φ;
and constructing and obtaining an elastic-plastic constitutive model based on the suspended particle phase according to the yield surfaces corresponding to the first yield condition, the second yield condition and the third yield condition respectively. FIG. 2 is a schematic representation of the yield surface provided by the present invention, the yield surface corresponding to each of the three yield conditions (i.e., f)1、f2And f3) As can be seen with reference to fig. 2, in the first yield condition, the factor before pressure is a function of shear rate
And an increase in the suspended particle volume fraction phi; the pressure is limited by the third yield condition, when phi is less than or equal to phimWhile, the same is true with shear rate
Is increased with an increase in; at phi > phimThe pressure is no longer limited and can be increased to any value, which means that during shearing, an unlimited increase in pressure causes an unlimited increase in the shear stress τ, so that a blocking phenomenon occurs.
According to the invention, an elastoplastic constitutive model which is correspondingly obeyed by suspended particles is designed according to the plastic shear stress and the volume change of the non-Newtonian fluid, and in the model, the internal stress of the suspended particle phase is limited by the product of pressure and friction coefficient, and is simultaneously influenced by the shear rate, the volume fraction of the suspended particle phase and the like, thereby forming a relatively complete description of the physical properties of the suspended body.
On the basis of the above embodiment, the formula of the friction function is:
φm＝φj+(φc-φj)Ψ；
wherein the content of the first and second substances,
representing the friction function of the particle after a change in the skeletal structure, cfA constant indicating a control change rate, H indicates a hardening rate,
represents the plastic shear rate; ΨmRepresenting the maximum value of the friction function, psi representing the friction function before the change of the particle bone structure, the friction function being defined in the interval 0, psim]To (c) to (d); ξ denotes the buckling coefficient, τ denotes the shear stress, τ*Denotes the repulsion constant between particles, cbAnd l is a constant, phi, controlling the buckling effectmDenotes the maximum suspended particle phase volume fraction, phi denotes the suspended particle phase volume fraction, phicIs indicative of phimLower bound of (phi)jIs indicative of phimThe upper bound of (c). In the present invention, the friction function directly affects the maximum allowable volume fraction φmAnd in turn, the rheological behavior of the material.
In the present invention, psi is usedmWhen Ψ increases, meaning that the friction between suspended particles increases, the maximum volume fraction allowed decreases, going towards φcClose, and phi does not change. When phi ismDecreasing to near φ, a large increase in viscosity occurs, causing discontinuous shear thickening. FIG. 3 is a schematic diagram of three shear thickening rheology mechanisms provided by the present invention, as shown in FIG. 3, there are 3 rheology zones when φ<φcAny shear rate is permissible; when phi isc<φ<φjWhen the shear rate increases, the friction function increases, resulting in phimIf is less than phi, the blockage will be caused, therefore the shearing rate must be less than a certain threshold value; when phi is more than phijWhen the fluid is blocked, any shear flow is unlikely to occur.
The invention describes the proportion of the suspended particle phase and the liquid phase in the space by volume fraction, the volume fraction has key effect on the characteristics of the suspension, wherein, the volume fraction of the suspended particle phase is marked as phi, which describes the density degree of the space occupied by the suspended particle phase, and the volume fraction of the liquid phase at the same position is 1-phi according to the definition. In the present invention, the equivalent viscosity of the suspension increases with increasing φ and approaches φmWhen phi is larger than or equal to phi, the temperature is greatly increasedmA blocking phenomenon occurs and the material cannot flow in shear.
On the basis of the above embodiment, the method further includes:
and carrying out discrete simulation solution on the elastic-plastic constitutive model by a material point method to obtain the rheological property of the non-Newtonian fluid.
In the invention, a material dot method is adopted for simulation, and the specific steps are as follows:
step 201, interpolating the mass and the speed of the particles on a grid, and calculating the pressure gradient and the internal stress;
step 202, updating grid speed and applying boundary conditions;
step 203, interpolating the updated grid speed back to the particle, updating the position of the particle, and calculating the speed gradient of the position of the particle;
step 204, updating the stress tensor carried by the suspension phase particles, and calculating the pressure of the liquid phase particles;
step 205, obtaining the shear rate according to the elastic-plastic yield condition of the suspension phase
Shear stress tau and pressure p, from which the friction function psi and the maximum volume fraction phi of the suspended phase particles are updatedm；
And step 206, repeating the steps 201 to 205 until the algorithm is ended.
On the basis of the above embodiment, the discrete simulation solution is performed on the elastic-plastic constitutive model by a material point method, and the method further includes:
simulating the permeation between the liquid and the dry particles based on a liquid drift velocity model, the liquid drift velocity model being:
wherein, cdDenotes the diffusion constant,. phifIndicating the liquid phase volume fraction.
In the present invention, in order to simulate the penetration between the liquid and the dry particles, the present application introduces diffusion based on a drift velocity model when interpolating the updated mesh velocity back to the particles (i.e., step 203 in the above-described embodiment), thereby simulating the phenomenon of penetration diffusion between two phases.
On the basis of the above embodiment, the simulating the liquid phase and the suspended particle phase of the non-newtonian fluid based on the continuity equation and the momentum equation respectively includes:
simulating a suspended particle phase in the non-Newtonian fluid based on a solid continuity equation and a solid momentum equation, the solid continuity equation being:
the solid momentum equation is as follows:
wherein the content of the first and second substances,
represents the solid-phase equivalent density, ρsDenotes the solid phase density, t denotes the time, usRepresenting the suspended particle phase velocity, g representing gravity, fdRepresenting the fluid resistance, σsDenotes shear stress,. phisRepresents the solid phase volume fraction;
simulating a liquid phase in the non-Newtonian fluid based on a liquid continuity equation and a liquid momentum equation, wherein the liquid continuity equation is as follows:
the liquid momentum equation is as follows:
wherein phi isfRepresenting the liquid phase volume fraction, pfDenotes the liquid phase density, ufWhich is indicative of the velocity of the liquid phase,
denotes the liquid phase equivalent density, σfIndicating viscous stress. In the invention, the pressure of the fluid is fixed as follows from the momentum equation
The invention constructs a unified framework for simulating non-Newtonian fluids, and simulates various non-Newtonian fluids through physically interpretable parameters. When simulating a suspension of arbitrary volume fraction, the coupling between them can be easily simulated. The yield criterion and the friction function adopted by the invention provide an accurate physical tool and can simulate the discontinuous shearing thickening phenomenon. Finally, the present invention encompasses an osmotic diffusion mechanism that can mimic the mixing process between separate phases in their initial state, thereby mimicking the formation of non-Newtonian fluids.
Fig. 4 is a schematic structural diagram of a non-newtonian fluid simulation apparatus provided by the present invention, and as shown in fig. 4, the present invention provides a non-newtonian fluid simulation apparatus, which includes a first simulation module 401, a coupling module 402, a model building module 403, and a second simulation module 404, where the first simulation module 401 is configured to respectively simulate a liquid phase and a suspended particle phase of a non-newtonian fluid based on a continuity equation and a momentum equation; the coupling module 402 is configured to couple the liquid phase and the suspended particle phase according to a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of a property between the liquid phase and the suspended particle phase; the model construction module 403 is configured to construct an elasto-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model; the second simulation module 404 is configured to construct a friction function according to the particle skeletal structure variation of the two-phase suspension model, and add the friction function to the elasto-plastic constitutive model for simulating the rheological properties of the non-newtonian fluid.
The non-Newtonian fluid simulation device provided by the invention provides a non-Newtonian fluid simulation method with higher expansibility, the simulation of non-Newtonian properties is realized by modeling a real physical mechanism of the bottom layer of the non-Newtonian fluid simulation device, and parameter control which can be interpreted physically is provided, so that different types of non-Newtonian fluids are simulated uniformly, and the rheological property of the non-Newtonian fluids is accurately described.
The apparatus provided by the present invention is used for executing the above method embodiments, and for details and flow, reference is made to the above embodiments, which are not described herein again.
Fig. 5 is a schematic structural diagram of an electronic device provided in the present invention, and as shown in fig. 5, the electronic device may include: a processor (processor)501, a communication interface (communication interface)502, a memory (memory)503 and a communication bus 504, wherein the processor 501, the communication interface 502 and the memory 503 are communicated with each other through the communication bus 504. Processor 501 may invoke logic instructions in memory 503 to perform a non-newtonian fluid simulation method, the method comprising: respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation; coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase; constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model; and constructing a friction function according to the particle skeletal structure change of the two-phase suspension model, and adding the friction function into the elastic-plastic constitutive model for simulating the rheological property of the non-Newtonian fluid.
In addition, the logic instructions in the memory 503 may be implemented in the form of software functional units and stored in a computer readable storage medium when the logic instructions are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-only memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
In another aspect, the present invention also provides a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the non-newtonian fluid simulation method provided by the above methods, the method comprising: respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation; coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase; constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model; and constructing a friction function according to the particle skeletal structure change of the two-phase suspension model, and adding the friction function into the elastic-plastic constitutive model for simulating the rheological property of the non-Newtonian fluid.
In yet another aspect, the present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor is implemented to perform the non-newtonian fluid simulation method provided in the above embodiments, the method comprising: respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation; coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase; constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model; and constructing a friction function according to the particle skeletal structure change of the two-phase suspension model, and adding the friction function into the elastic-plastic constitutive model for simulating the rheological property of the non-Newtonian fluid.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. A method of simulating a non-newtonian fluid, comprising:
respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation;
coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase;
constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model;
and constructing a friction function according to the particle skeletal structure change of the two-phase suspension model, and adding the friction function into the elastic-plastic constitutive model for simulating the rheological property of the non-Newtonian fluid.
2. A non-newtonian fluid simulation method according to claim 1, wherein the fluid resistance formula is:
wherein k isdDenotes the resistance constant, usDenotes the suspended particle phase velocity ufDenotes the liquid phase velocity, d denotes the suspended particle diameter, eta denotes the fluid viscosity, phisRepresents the suspended particle phase volume fraction;
the fluid pressure equation is:
wherein p isfDenotes the liquid phase density, pf0Denotes the liquid phase static density and κ denotes the stiffness coefficient.
3. The non-Newtonian fluid simulation method of claim 1, wherein the constructing an elasto-plastic constitutive model based on suspended particle phase according to the plastic shear stress and volume change of the two-phase suspension model comprises:
from the plastic shear stress, a first yield condition is established:
τ≤(μ+β)p；
wherein τ represents shear stress, μ represents friction coefficient, IvDenotes the viscosity number, phimRepresents the maximum suspended particle phase volume fraction, beta represents the expansion angle, p represents the pressure,
representing the plastic shear rate, eta the liquid viscosity coefficient, mu1Denotes the viscosity number IvCoefficient of friction, mu, to 02Denotes the viscosity number IvCoefficient of friction to ∞, I0Is a constant parameter;
from the plastic stretching, a second yield condition is established:
p+∈≥0；
wherein epsilon represents a preset viscosity threshold value;
from the plastic compression, a third yield condition is established:
wherein φ represents the suspended particle phase volume fraction, and g (φ) represents a coefficient that varies with φ;
and constructing and obtaining an elastic-plastic constitutive model based on the suspended particle phase according to the yield surfaces corresponding to the first yield condition, the second yield condition and the third yield condition respectively.
4. A non-newtonian fluid simulation method according to claim 1, wherein the friction function is formulated as:
φm＝φj+(φc-φj)Ψ；
wherein the content of the first and second substances,
representing the friction function of the particle after a change in the skeletal structure, cfA constant indicating a control change rate, H indicates a hardening rate,
representing the plastic shear rate, ΨmRepresenting the maximum value of the friction function, psi representing the friction function before the change of the particle skeleton structure, xi representing the buckling coefficient, tau representing the shear stress, tau*Denotes the repulsion constant between particles, cbAnd l is a constant, phi, controlling the buckling effectmDenotes the maximum suspended particle phase volume fraction, phi denotes the suspended particle phase volume fraction, phicIs indicative of phimLower bound of (phi)jIs indicative of phimThe upper bound of (c).
5. A non-newtonian fluid simulation method according to claim 1, further comprising:
and carrying out discrete simulation solution on the elastic-plastic constitutive model by a material point method to obtain the rheological property of the non-Newtonian fluid.
6. A non-Newtonian fluid simulation method according to claim 5, wherein the elasto-plastic constitutive model is solved by discrete simulation by a particle method, the method further comprising:
simulating the permeation between the liquid and the dry particles based on a liquid drift velocity model, the liquid drift velocity model being:
wherein, cdDenotes the diffusion constant,. phifIndicating the liquid phase volume fraction.
7. A method for modeling a non-newtonian fluid according to claim 1, wherein the modeling the liquid phase and the suspended particle phase of the non-newtonian fluid based on the continuity equation and the momentum equation, respectively, comprises:
simulating a suspended particle phase in the non-Newtonian fluid based on a solid continuity equation and a solid momentum equation, the solid continuity equation being:
the solid momentum equation is as follows:
wherein the content of the first and second substances,
represents the solid-phase equivalent density, ρsDenotes the solid phase density, t denotes the time, usRepresenting the suspended particle phase velocity, g representing gravity, fdRepresenting the fluid resistance, σsDenotes shear stress,. phisRepresents the solid phase volume fraction;
simulating a liquid phase in the non-Newtonian fluid based on a liquid continuity equation and a liquid momentum equation, wherein the liquid continuity equation is as follows:
the liquid momentum equation is as follows:
wherein phi isfRepresenting the liquid phase volume fraction, pfDenotes the liquid phase density, ufWhich is indicative of the velocity of the liquid phase,
denotes the liquid phase equivalent density, σfIndicating viscous stress.
8. A non-newtonian fluid simulation device, comprising:
the first simulation module is used for respectively simulating a liquid phase and a suspended particle phase of the non-Newtonian fluid based on a continuity equation and a momentum equation;
the coupling module is used for coupling the liquid phase and the suspended particle phase through a fluid resistance formula and a fluid pressure formula to obtain a two-phase suspension model of the property between the liquid phase and the suspended particle phase;
the model construction module is used for constructing an elastic-plastic constitutive model based on the suspended particle phase according to the plastic shear stress and the volume change of the two-phase suspension model;
and the second simulation module is used for constructing a friction function according to the particle skeletal structure change of the two-phase suspension model and adding the friction function into the elastic-plastic constitutive model so as to simulate the rheological property of the non-Newtonian fluid.
9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor when executing the computer program implements the steps of the non-newtonian fluid simulation method of any of claims 1-7.
10. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the steps of the non-newtonian fluid simulation method according to any one of claims 1 to 7.
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