CN109800469A - The analog simulation method that more particle chain grain equilibrium spacing are predicted based on IB-LB method - Google Patents
The analog simulation method that more particle chain grain equilibrium spacing are predicted based on IB-LB method Download PDFInfo
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Abstract
A kind of analog simulation method predicted based on IB-LB method more particle chain grain equilibrium spacing is carried out the accurate transmission to information between fluid-solid and realizes the accurate description flowed to solid by using immersed Boundary Method；By adjusting model parameter to construct different operating conditions, then distribution of particles situation in Micro-flows is simulated under different operating conditions, i.e. axial and longitudinal crucial distributing position and grain spacing size, and then disengaged position and cross frequence are provided to realize the manipulation and packing of particle.The present invention can accurately and efficiently sub-elect target object from sample to be monitored and carry out accurately guidance and prediction.
Description
Technical field
It is specifically a kind of that boundary-lattice (are immersed based on IB-LB the present invention relates to a kind of technology of field of fluid mechanics
Sub- Boltzmann Immersed Boundary-Lattice Boltzmann) method convection current dynamic stability particle chain spacing size into
The analogy method of row prediction.
Background technique
The integrations such as arrangement, enrichment, screening, separation and capture of particle under minute yardstick may be implemented in microfluidic chip technology
Process, obtains huge advance in recent years, and development opens the new page of the numerous areas such as biology, chemistry and medicine.Such as
The real-time test analyzer (POCT) for serving clinic diagnosis, is capable of every physiology, the pathological parameter of real-time detection patient, is disease
Disease diagnosis and state of an illness detection provide valuable help.Such as water quality detection micro-system based on MEMS technology, in terms of water pollution control
It plays an important role.The key of microfluidic chip technology is how to manipulate the particulate matter in fluid to carry out to it effectively
Accurately separate.The method having proposed at present is mainly separated by dielectrophoresis, magnetic field separation, sound wave separation and hydrodynamics
The main paths such as separation.But either magnetic field or current field condition require additional stress and are adjusted to particle flow,
Its economy needs to be considered in the long term.And take hydrodynamics acquisition mode, then be only by particle by fluid matasomatism and
Other additional field of forces are not considered, to become optimal selection mode.
The method that common micro-fluidic chip particle applied fluid mechanics passively separates at present has an inertia effect separation, i.e., according to
It takes special shape to handle runner according to particle flow inertia characteristics, achieves the separation of different size particle.Its pipeline shape
May also can there be larger difficulty shape multiplicity, design processing accurate-size microchannel, and such as more labyrinthine passageways need to realize accurate vorticity
Value is to control particle flow.In addition there are lateral displacement methods, make different particle flow velocity sides by designing cylinder blocking structure
To there is difference to realize that particle separates.This method need to design polycylindser barrier channel, and cost consumption is huge.And it relies on
The method that special shape pipeline carries out particle flow control also dissociated deviation can occur with the abrasion of pipeline, be not most preferably to select
It selects.Therefore method the simplest be then by the self organization phenomenon of the generation in the restricted clearance of particle microchannel, thus
So that there is certain arrangement rule when particle flows in a fluid to separate particle.Particle self organization phenomenon refers to only by fluid
Flow velocity difference and inertia effect particle can migrate in straight runner to given crosswise and lengthwise position, and specific at this at this time
Position, which carries out specific frequency sampling, can be realized efficiently separating for particle.The key problem in technology is accurately to determine distribution of particles position
And grain spacing, so that it is determined that cross frequence realizes the packing of particle.And research workers are mostly focused on research list at present
The research in particle flow flow field and the simulation in particle migration path or the arrangement of more particle swarms are analyzed, rare to individual particle chain
Between specific particle arrangement and pitch problems discussion, and this exactly carries out the crucial letter of particle separation in micro-fluidic chip
Breath.
Lattice Boltzmann Method (Lattice Boltzmann Method) has been sent out so far as effective simulation means
It has opened up more than 20 years, has had been obtained and be widely recognized as in minute yardstick field.Different from the CFD approach of traditional analog fluid motion,
Its principle does not lie in discrete macroscopic view NS equation, but simulates the movement of fluid by solving discrete Boltzmann equation.Its base
In Molecule Motion Theory, there is the physical background of very clear and definite, macroscopically belonging to discrete method, and belongs on microcosmic
Continuation method, therefore it can preferably be applied to minute yardstick field, such as the flowing and heat exchange of fluid, the generation of crystal and
The research etc. of porous media.For immersed Boundary Method after after decades of development, modern scholar constantly carries out improvement to it makes it
More suitable for the flowing of simulation complex object and fluid structurecoupling problem.It takes two nested grids, flows to mobile solid boundaries and flow field
Body point takes independent Lagrangian points and Euler's point, is realized by the information exchange between two nested grids and is made between object and fluid
Phase mutual feedback firmly, therefore there is inherent advantage when analog stream consolidates problem.
The coupling between solid-liquid may be implemented using immersed Boundary Method coupling lattice Boltzmann method, accurate description goes out
The mathematical model of limited bulk particle and liquid phase fluid interaction and microcosmic transmitting, the flow field of microcosmic vortex structure is emulated with this
Mechanism of action between distribution, Interface Moving, hydraulic action and particle chain, thus in certain flow rate or certain granules size
Under the conditions of distribution to particle chain, such as laterally and longitudinally position, the axial spacing that is distributed provides determining numerical value, to realize direct current
The high efficiency and accuracy of pipeline endoparticle packing.Micro-fluidic chip system can not need external force assistance under this simulation and prediction
And realize the controllable prediction of particle, the flow channel of design complex configurations is not needed yet, thus production cost is greatly reduced, it realizes
The particle of high-efficiency and economic dispenses.
Summary of the invention
The present invention is directed to crucial shortcoming of the prior art on application problem, proposes a kind of based on IB-LB method pair
The analog simulation method that more particle chain grain equilibrium spacing are predicted predicts micromation real-time monitoring point by using this method
Spacing size is balanced in analysis system between monitoring object axis vertical distributing position and particle, to separate to long straight pipeline particle
Provide determining disengaged position and cross frequence.
The present invention is achieved by the following technical solutions:
By the present invention in that being carried out the accurate transmission with immersed Boundary Method to information between fluid-solid and being realized to solid flowing
Accurate description.By adjusting model parameter to construct different operating conditions, such as granular size, line size and fluid flow rate.Then
Simulate under different operating conditions distribution of particles situation in Micro-flows, i.e., it is axial big with longitudinal key distributing position and grain spacing
It is small, and then disengaged position and cross frequence are provided to realize the manipulation and packing of particle.
The flow field refers to: three-dimensional pressure drives flow model.Study and be most widely used in micro-fluidic chip i.e.
For pressure-driven stream, i.e., there are flowings when pressure difference inside microfluid.Therefore real using the method for outer power drive in simulations
Existing Poiseuille flow, and the speed shear gradient generated in this case is so that particle lateral transfer carries out tissue arrangement certainly in turn
Necessary condition.
The pretreatment refers to: when initial flow-field, taking particle swarm movement initial velocity identical as flowing initial velocity
Pretreatment.Can initial velocity be 0 or giving certain initial velocity accelerates evolutionary process.The release original shape of particle swarm is then
For along the particle chain or ipsilateral or heteropleural for flowing to unequal spacing, spacing is in 2D to 5D etc..
The accurate description to solid flowing, is accomplished by the following way: fluid point information, example near integrated solid
Such as the speed on three-dimensional, it is handled using delta function, obtains the preliminary discreet value of speed on solid point；So
The restoring force on solid point, that is, Lagrangian points is calculated afterwards.By this restoring force it is discrete after acquire flow field point i.e. Euler's point physical strength.It is logical
It crosses the revised flow field physical strength stream field and carries out speed amendment, complete the reciprocal effect of particle and flow field.
It includes fluid velocity that information, which includes: the interaction variable being related in immersed Boundary Method, between the fluid-solid
Uijk, solid speed Us, solid boundaries restoring force Fs, revised fluid physical strength etc..
The model parameter includes: flow velocity U (Ux, Uy, Uz), particle size D, particle is initially arranged and duct length
(grain density), slack time τ, line size LWH.
The feedback processing refers to: by adjusting model parameter such as duct length, granular size, fluid flow rate is to construct
Then different operating conditions simulate under different operating conditions distribution of particles rule in Micro-flows, become further according to a certain parameter of different models
It measures lower balance granules chain distribution and provides the regularity of distribution, and then predict grain spacing size when actual process results, that is, actual separation.
Technical effect
Compared with prior art, the technical effect of industrial circle of the present invention includes: that the present invention can provide current for the first time
The bottleneck problem encountered when grain packing, i.e. particle arrangement position and grain spacing, thus can be with the packing particle of effective.This
Invention can be distributed feelings in the case where providing the known conditions of target isolate size and pipe flow speed with Accurate Prediction particle in runner
Condition gives certain directive function to particle packing, promotes particle packing that can efficiently carry out under the conditions of having controlled orderly.
Detailed description of the invention
Fig. 1 is that simulation basic flow chart is solved using LBM method；
Fig. 2 is immersed Boundary Method schematic diagram；
Fig. 3 is D3Q19 schematic diagram；
Fig. 4 is research model schematic diagram；
Fig. 5 is heteropleural particle chain particle initial release position i.e. arrangement situation and distance computation method schematic diagram；
Fig. 6 is ipsilateral particle chain initial release position and distance computation method schematic diagram；
Fig. 7 is direct current pipeline particle packing experiment schematic diagram in micro-fluidic chip；
Particle arrangement situation tests result schematic diagram corresponding with emulation under the same flow velocity granular size of Fig. 8；
Fig. 9 is that ipsilateral particle is tested and analog result distribution map under certain flow rate；
In figure: a is experiment, and b is analog result；
Figure 10 is that ipsilateral particle (Rep2) spacing changes over time situation statistics schematic diagram；
In figure: a is that spacing floating then thinks that stable headway cannot be formed, and b stablizes same numerical value for spacing presentation and then judges
Stable headway particle chain is formed；
Figure 11 is square duct endoparticle equilbrium position distribution map；
Figure 12 is particle longitudinal balance arrangement distribution map under variable grain Reynolds number and density；
Figure 13 is spacing regularity of distribution schematic diagrames ipsilateral and that heteropleural particle chain is under different densities and different Reynolds number；
In figure: a be it is ipsilateral, b is heteropleural.
Specific embodiment
As shown in Figure 1, this embodiment realizes accurate fluid structurecoupling by using IB-LB method, to accurately simulate
Fluid flowing law and more particle characteristics of motion.
As shown in Fig. 2, for immersed Boundary Method schematic diagram used by emulation mode.Immersed Boundary Method divides fluid and solid
It leaves and, fluid is indicated with Eulerian mesh, i.e. dotted portion in figure.Solid then indicates with Lagrangian mesh point, as black in figure
Color curve indicates solid boundaries.Information friendship is carried out using delta function in this way between Euler's lattice point and Lagrangian lattice point
It changes.
As shown in figure 3, the model D3Q19 taken by LATTICE BOLTZMANN, i.e., each grid point has 19 on three dimension scale
A migratory direction.
As shown in Fig. 4, Fig. 5 and Fig. 6, all arrangement situations being likely to occur when particle flow to be simulated are needed for this,
Two kinds of situations are flowed with particle heteropleural with the flowing of particle unilateral side, it is ensured that the comprehensive and accuracy of emulation.
The present embodiment specific steps include:
Step 1) initializes threedimensional model, realizes poiseuille flowing and release particle in rectangular or square channel.
The initialization refers to: setting gradually initial velocity U (x, t) is 0, initial balance distribution function feq(x, t) is
0, initial distribution function f (x, t) is 0 and particle information, defines integral macroscopic parameter.
The particle information includes: particle initial velocity Up0, initial release position Xp,Yp,Zp, initial release space D can
It controls (2D~4D), granular size R (0.2H~0.4H).
The integral macroscopic parameter includes: particle and fluid density ρfAnd ρs, viscosity μ, slack time τ, at the beginning of flow field
Beginning speed u0, v0, w0, flow field length, width and height size L, W, H, external force fbTo drive enough speed.
The initialization can be speed return-to-zero in the present embodiment or assigning its initial velocity makes it develop
Journey is accelerated, in which: the balance function of each grid point under grid system are as follows:Its
In: ciFor different directions particle discrete velocity, csIt is the model velocity of sound, size isωiFor different directions weight coefficient, foundation
Selected model is different and different.
Consideration can not press the flow field problem of Newtonian fluid, the governing equation of the threedimensional model are as follows: adhesive can not flow
Dynamic quality, momentum conservation equation:WithWherein: ρ, u, p, μ points
Not Wei fluid density, speed, pressure and coefficient of kinetic viscosity, fbAnd fsIt is body force suffered by unit volume fluid, fbWith
To drive fluid in pipeline to flow to form fully developed Poiseuille flow, fsEffect be realize immerse boundary on without sliding velocity
Boundary condition.
Upon initialization, the lattice Boltzmann method includes:
1. the collision and migration of grid point, in which: collision process use applies source item but loose BGK collision model, protects
Demonstrate,prove the driving speed of pipeline:
Fi(x, t) is power source item, for driving pipe flow speed to realize Poiseuille flow: Δ t is the unit collision time, and F (x, t) is physical strength, that is, fbA constant value is taken for flow velocity direction.Collision
It is to carry out the important step of lattice Boltzmann method with migration, molecular mass, momentum and the conservation of energy in collision, therefore can
To obtain collision front and back molecule friction speed, the function after collision is migrated, evolution finishes each variable of next time step.
2. boundary processing method.Since model need to simulate unlimited long pipeline, this can not be simulated in an experiment, the present embodiment
Using inlet and outlet period flox condition, particle can be simulated in the flowing of unlimited long pipeline.Other boundaries are all made of the rebound of half step
Cycle boundary format.
3. carrying out fluid structurecoupling process using immersed Boundary Method: real by introducing Dirac delta function δ [x-X (s, t)]
The information exchange of existing Eulerian coordinates and Largrangian coordinates physical quantity.It calculates first and does not reinforce source item flow field spot speed:Lagrangian points movement speed is estimated to obtain with this speed
It the solid speed estimated by flow field point and estimates speed and acquires solid point stressFinally
One step is modified by solid point stress stream field speed: first acquiring flow field point feedback force Fluid erection rate is being calculated with this powerWherein, UdFor the desired speed of next time step, UnoF
It is then not apply to immerse the interim speed that bounding volumes power obtains.Subscript ijk indicates the unit quantity at Euler's point, and subscript b is indicated
The unit quantity of Lagrangian points.H is particle units area.Delta function D is
R is that Lagrangian points nearby choose certain flow field regions to granular center distance.
4. counting interparticle distance.The X between adjacent particles, tri- direction spacing of Y, Z are counted simultaneously, and total spacing isTwo judgements need to be carried out when wherein counting spacing situation of change: being judged between particle and particle and wall
Whether can collide between face, if collision uses collision model；Judge whether spacing changes acutely, if meeting certain condition
Judge that spacing is stablized to stop calculating, continues to return to impacting step if not meeting.
According to the analog result of above-mentioned lattice Boltzmann method, particle chain is obtained in specific distribution laterally and longitudinally
Rule specifically includes:
A. for square pipe common in device, particle is easily distributed at conduit axis, that is, will form four stabilizations
Lengthwise position, such as Figure 11.But grain equilibrium position then depends on fluid flow rate and granular size with a distance from wall surface.This emulation
Determining numerical value is provided, by the equilbrium position for consulting the available particle chain of attached drawing 12.Such as in Rep=6, granular size is section
When length 0.4, when density is 0.25, neutral buoyancy position and pipeline ratio are at 0.255.
Axial spacing after particle chain is stable, equally also needs the prerequisites such as fluid flow rate, granular size.And grain spacing
Also have with pipeline endoparticle density compared with Important Relations.This emulation discovery flowing spacing is by whirlpool between particle away from determining, then whirlpool away from
It is similarly dependent on above-mentioned three kinds of variable situations.Such as attached drawing 12, balance when ipsilateral particle arrangement is arranged with heteropleural particle is respectively indicated
Spacing size is with fluid flow rate (Rep) and grain density (lf) schematic diagram.From the particle that can be determined in this figure under certain operating condition
Spacing obtains the separation spacing time that should be taken when particle packing and cross frequence by speed conversion.
B.1. for the particle chain of arrangement ipsilateral in micro-fluidic chip, under the flow operating mode, intergranular arrangement is with flow velocity
The bigger number the more unstable, causes spacing to maintain the fluctuation of certain amplitude always, as shown in Figure 10 a figure；But control is in a constant current
When fast, stable particle spacing can be formed between particle, longitudinal pitch, which does not change, yet at this time reaches stable.Therefore, it controls
Can good flowing velocity for form stable particle chain with great influence, and for partial size ratio, (particle diameter is straight with pipeline hydraulic
The ratio between diameter) be 0.4 particle for, it is proposed that otherwise particle Reynolds number can not form particle stable in directive significance less than 12
Chain.And in the range of particle Reynolds number is 2-9, change fluid flow rate is unobvious to effect of distance, therefore can be according to experiment
Working condition under practical equipment selects most suitable flow velocity processing, to obtain best packing frequency and packing position.
B.2 no matter ipsilateral flowing or heteropleural is presented in particle swarm in chip pipeline, and grain density is excessive to be unfavorable for particle
Steady flow in pipeline.But lower critical density different in flow rate is different.When particle Reynolds number is 2 or 3, critical density lf is
0.45, stable particle chain can not be then formed higher than this value, also can not just carry out accurate particle manipulation and packing.When particle Reynolds
Number be promoted to 6, when which rises to 0.4. and is promoted to 9 maximum manipulation grain density must not exceed 0.3. (above with
Partial size ratio is for 0.4 particle)
B.3. under optimum flow rate (Rep2~Rep6), fluid flow rate is between the arrangement micro-fluidic chip endoparticle without larger
Which kind of influence, but grain density then then has a major impact as shown in Figure 13 a and b to grain spacing, either flow velocity, between basic
Away from all with the linear distribution of density, and spacing differs in 2-4 interparticle distance, detailed data can be obtained by consulting this figure.
As Rep is 6 grain densities be 3 when stable particle spacing be 3.3D, and Rep be 3 when can reach same effect.Therefore, practical work
Most suitable duct length and grain spacing can be selected according to cost under condition, carry out the separation of particle.
It is more common in actual techniques flowing in c heteropleural particle flow mode.When pipeline grain density is greater than 0.45, no
Different stable particle arrangement spacing are corresponded to density, therefore cross frequence is mainly determined by grain density at this time, fluid flow rate
Flowing to equilbrium position not to particle at this moment influences.And work as density as low as certain value (0.45), grain spacing is no longer with particle
Variable density, but change with water velocity and change.Therefore cross frequence is not influenced by grain density at this time, and is mainly considered
Pipe flow speed.Figure 13 b gives partial size than changing atlas for the spacing of 0.4 lower particle, can obtain certain item by consulting the figure
Particle arrangement is estimated under part.Therefore under actual condition, grain density has very important influence, grain density mistake for spacing
Small spacing is excessive by flow control, is controlled by duct length, therefore in a practical situation, need to recognize turnover density for point
The decisive action of off-frequency rate need to first determine the turnover density of pipeline, consider various influence factors, Jin Erxuan further according to actual conditions
Select suitable actual condition.
Above-mentioned specific implementation can by those skilled in the art under the premise of without departing substantially from the principle of the invention and objective with difference
Mode carry out local directed complete set to it, protection scope of the present invention is subject to claims and not by above-mentioned specific implementation institute
Limit, each implementation within its scope is by the constraint of the present invention.
Claims (4)
1. a kind of analogy method predicted based on IB-LB method more particle chain grain equilibrium spacing, which is characterized in that logical
It crosses using immersed Boundary Method, the accurate transmission is carried out to information between fluid-solid and realizes the accurate description flowed to solid；Pass through
Model parameter is adjusted to construct different operating conditions, then simulates under different operating conditions distribution of particles situation in Micro-flows, i.e., axially
With longitudinal crucial distributing position and grain spacing size, and then provide disengaged position and cross frequence with realize the manipulation of particle with
Packing；
The flow field refers to: three-dimensional more particle Poiseuille flow movable models；
Information includes: fluid velocity, solid speed, solid boundaries restoring force and revised stream between the fluid-solid
Body physical strength；
The model parameter includes: that duct size, fluid flow rate, particle size, particle are initially arranged and pipeline is long
Degree, i.e. grain density, slack time and line size；
The accurate description to solid flowing, is accomplished by the following way: fluid point information near integrated solid uses
Delta function carries out interpolation to it, obtains the preliminary discreet value of speed on solid point；Then solid point, that is, Lagrangian points are calculated
On restoring force, and by this restoring force it is discrete after acquire flow field point i.e. Euler's point physical strength；Pass through the revised flow field physical strength again
Stream field carries out speed amendment, completes the reciprocal effect of particle and flow field.
2. according to the method described in claim 1, it is characterized in that, it is described by using immersed Boundary Method, to fluid-solid it
Between information carry out the accurate transmission, specifically include:
1. the collision and migration of grid point, in which: collision process using apply source item but relaxation BGK collision model, guarantee pipe
The driving speed in road:Wherein: Fi(x,
It t) is power source item, for driving pipe flow speed to realize Poiseuille flow: Δ t is the unit collision time, and F (x, t) is physical strength, that is, fbA constant value is taken for flow velocity direction；
2. boundary processing method, the flowing using inlet and outlet period flowing condition simulation particle in unlimited long pipeline, other boundaries
It is all made of half step rebound cycle boundary format；
3. carrying out fluid structurecoupling process using immersed Boundary Method, Europe is realized by introducing Dirac delta function δ [x-X (s, t)]
It draws the information exchange of coordinate and Largrangian coordinates physical quantity: calculating do not reinforce source item flow field spot speed first:Lagrangian points movement speed is estimated to obtain with this speed
It the solid speed estimated by flow field point and estimates speed and acquires solid point stressSo
It is modified afterwards by solid point stress stream field speed: first acquiring flow field point feedback force fijk(x, t)=∫bfbD[Xijk-Xb]ds
Fluid erection rate is being calculated with this powerWherein, UdFor the desired speed of next time step, UnoFIt is then
Do not apply and immerse the interim speed that bounding volumes power obtains, subscript ijk indicates the unit quantity at Euler's point, and subscript b indicates glug
The unit quantity of Lang Dian, h are particle units area；
4. counting interparticle distance: while counting the X between adjacent particles, tri- direction spacing of Y, Z, total spacing are as follows:
Two judgements need to be carried out when wherein counting spacing situation of change: judging whether can touch between particle and between particle and wall surface
It hits, if collision uses collision model；Judge whether spacing changes acutely, judges that spacing is stablized if meeting certain condition and stop meter
It calculates, continues to return to impacting step if not meeting.
3. according to the method described in claim 2, it is characterized in that, the Dirac delta functionWherein: r is that Lagrangian points nearby choose certain flow field regions into particle
Heart distance.
4. according to the method described in claim 1, it is characterized in that, the reciprocal effect of the particle and flow field, including particle chain
In the specific regularity of distribution laterally and longitudinally, obtained especially by following manner:
A. for square pipe: particle is easily distributed at conduit axis, forms four stable lengthwise positions, the position is away from pipeline
The length on boundary changes with the variation of reynolds number Re and particle size；Particle size increases, then longitudinal balance position is closer
On the outside of pipeline；Flow velocity is improved, then then has the tendency that first increasing reducing afterwards away from wall surface position, turnover Reynolds number is 100-200；
B. the axial position after stablizing for particle chain, specifically includes:
B.1. for ipsilateral stable particle chain, i.e. particle flow does not have only along axial side and crosses axis to other side particle
Situation: for partial size ratio, i.e., for the particle that particle diameter and pipeline hydraulic diameter ratio are 0.4, particle Reynolds number is less than etc.
In 9；
B.2. the increasing degree of grain density, i.e. duct length reduces with density, spacing in 2-5 interparticle distance, spacing with
The reduction of grain density and increase；
C. for heteropleural particle: spacing determines that vorticity can be mutually influenced in upper-lower axis by vorticity size between particle, into
And it is not consistent with ipsilateral vorticity size under identical working condition: when density is (0.45~0.8) particle stabilized spacing it
Between be not change with Rep, when density as low as 0.45, grain spacing no longer changes with grain density, but with water velocity
Change and changes.
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