CN106021638A - Modelling method for bubbling fluidized bed based on random motion of bubbles and particles - Google Patents
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Abstract
The invention discloses a modelling method for a bubbling fluidized bed based on random motion of bubbles and particles. The method comprises the steps that (1) statistics for particle motion rules of the bubbling fluidized bed computed by CFD-DEM is carried out, and a Markov chain random model of a particle phase is established; (2) image identification is carried out to an instant distribution map of the bubbling fluidized bed particles computed by the CFD-DEM, statistics is carried out to rules for generation, motion and growth of the bubbles, and a bubble random development model is established; and (3) a baseball cap model of bubble shapes is used to couple the particle-phase Markov course with the bubble random model, and a random model of the particle motion of the bubbling fluidized bed is established. The method disclosed by the invention has the advantages that the defect that a single particle-phase Markov course cannot reflect bubble information and influences of the information on the particle motion can be solved; and computation loads are greatly reduced, and a computation speed is increased on the premise of guarantee of accuracy of the bubbling fluidized bed particle motion.
Description
Technical field
The present invention relates to a kind of bubbling fluidized bed modeling method based on bubble and granule random motion, belong to gas-particle two-phase
Flow computer numerical simulation technology field.
Background technology
Bubbling fluidized bed has the highest heat transfer and rate of heat transfer, in chemical industry, the energy, food and medicine processing and other fields
Extensive application.Bubbling fluidized bed is carried out Computer Numerical Simulation and contributes to the optimization design of system, it is possible to significantly drop
Low experimentation cost.
Traditional experience and semiempirical model (such as plug flow model and bubbling tow phase model) computational efficiency are high, and model rings
Answering speed fast, but this class model cannot provide detailed bubble and particle motion rule, computational accuracy is the lowest.Currently a popular base
In Fluid Mechanics Computation and the method for numerical simulation of particle kinetics, because it is based on solving basic physics's formula, it is possible to relatively
For calculating the characteristics of motion of granule accurately, and concentration distribution etc., particularly Eulerian-Lagrangian Method considers gas phase
Interaction with granule phase.Wherein, CFD-DEM model also contemplates intergranular interaction so that it is can be the most accurate
Simulated gas fixed double phase flow, but calculate time length and calculated load height and be always this class model and amplify further and be applied to reality
Bottleneck.Stochastic model be then can the quick potential method of one of accurate simulation particle system, be based especially on CFD-
The Markov chain stochastic model of DEM result of calculation has that model is simple, sample information is enriched, calculate fireballing feature,
Preliminary Applications has been had in this kind of pure particle system of cylinder mixer.Interaction between bubbling fluidized bed gas-particle two-phase is very
Strongly, more there is the impact brought that occurs granule is moved of bubble, when using the method identical with being applied to pure particle system
When Markov chain stochastic model is applied to bubbling fluidization bed system, can only obtain the most macroscopical granule characteristics of motion, it is impossible to
Gas-particle two-phase flow pattern complicated in simulating bed.Find the impact that granule is moved by suitable method by bubble in bubbling fluidized bed
It is coupled with the Markov process of granule and becomes the key developing bubbling fluidized bed stochastic model further.
Summary of the invention
Goal of the invention: in order to overcome the deficiencies in the prior art, the present invention provide a kind of based on bubble and granule with
The bubbling fluidized bed modeling method of machine motion, the method establishes the random progressions model of bubble, bubble is moved granule
Impact couples with the Markov process of granule, sets up bubbling fluidized bed granule motion random model.Ensureing underload, quickly counting
While calculation, it is greatly improved bubbling fluidized bed stochastic model numerical stability.
Technical scheme: for achieving the above object, the technical solution used in the present invention is:
A kind of bubbling fluidized bed modeling method based on bubble and granule random motion, comprises the following steps:
Step 1, by bubbling fluidized bed grid division, the analog result of statistics early stage CFD-DEM model obtains distribution of particles
Figure.Calculate granule transition probability between grid, set up the Markov chain stochastic model of granule phase according to transition probability.Pass through
Markov chain stochastic model obtains particle position information.
Step 2, the distribution of particles figure obtaining CFD-DEM modeling carries out image recognition, adds up the generation of bubble, fortune
Rule that is dynamic and that grow up, sets up the random progressions model of bubble, determines that bubble phase is to position according to the random progressions model of bubble.
Step 3, utilizes the baseball cap model of bubble shape by the Markov chain stochastic model in step 1 and step 2
The random progressions model of bubble couples, and sets up the stochastic model of bubbling fluidized bed granule motion.By step 1) granule that obtains
Positional information and step 2) bubble phase that determines substitutes into the stochastic model of bubbling fluidized bed granule motion and obtains coupling gas position
The position of granule after bubble.
Preferred: the method for building up of Markov chain stochastic model described in described step 1, according to granule turning between grid
Move probability and build the Markov chain transition probability matrix of granule motion.It is calculated granule grid by transition probability matrix to believe
Breath, obtains particle position information by granule gridding information.
Preferred: the method for building up of the random progressions model of bubble in described step 2: statistics differing heights therapeutic method to keep the adverse QI flowing downwards alveolar substance respectively
Edema with the heart involved mean place and the probability distribution of equivalent diameter, probability distribution utilizes random number to simulate bubble in bubbling fluidized bed accordingly
Produce, moving and growing up obtains the random progressions model of bubble.
Preferred: the total number of bubble that described step 2 obtains in the random progressions model of bubble keeps constant in bed, bubble
Total number is determined by average bubble number in the bed of CFD-DEM modeling, when a bubble barycenter is increased beyond bed mean height
When spending, a new bubble i.e. produces bottom bed.Bubble constantly rises in evolution, grows up.
Preferred: granule is uniformly random distribution in grid.
Preferred: the baseball cap model of bubble shape in described step 3: the main body of bubble be radius be rtCircle C1 is by an equal basis
Remainder after the round C2 intercepting of size, including three parts, respectively first area I, second area II and the 3rd district
Territory III, the 3rd region III are that circle C2 intercepts the part of falling, and second area II is the arc that circle C2 intercepts in the part fallen on circle C2
And the two-end-point of this arc respectively with center of circle C1 line area defined, first area I is the circle remaining arc of C1 and this arc
Two-end-point respectively with center of circle C1 line area defined.
Preferred: to be in granule and the bubble generation coupling in three kinds of regions before coupling, be bubble top, bubble respectively
Bottom and bubble trailing vortex.
Preferred: near the bubble using Davison model to describe, the granule characteristics of motion calculates three kinds of regions particulate and gas
The coupling of bubble.
Beneficial effect: a kind of based on bubble and granule random motion the bubbling fluidized bed modeling method that the present invention provides,
Compared to existing technology, have the advantages that
The bubbling fluidized bed modeling method based on bubble and granule random motion of the present invention, by statistics bubbling fluidized bed
CFD-DEM analog result, it is thus achieved that granule and the characteristics of motion of bubble, establish the random development of bubbling fluidized bed bubble first
Model, and set up the baseball cap model of bubble shape, the Markov stochastic process of granule introduces the shadow that it is moved by bubble
Ring；Present invention, avoiding Fluid Mechanics Computation and the particle kinetics equation solving complexity, computational efficiency is greatly improved, with
Time, the random progressions model of bubble and granule Markov process couple the computational accuracy that ensure that bubbling fluidized bed stochastic model.
Accompanying drawing explanation
Fig. 1 is the baseball cap model of bubble shape and bubble and granule coupling algorithm schematic diagram.
Fig. 2 is that the bubble that statistics CFD-DEM result of calculation obtains produces probability distribution graph.
Fig. 3 is the bubble centroid position scattergram that statistics CFD-DEM result of calculation obtains.
Fig. 4 is that the statistics bubble diameter that obtains of CFD-DEM result of calculation is along height of bed scattergram.
Fig. 5 (a) is bubbling fluidized bed granule random motion design sketch before the coupling random progressions model of bubble.
Fig. 5 (b) is bubbling fluidized bed granule random motion design sketch after the coupling random progressions model of bubble.
Fig. 6 (a) is before and after stochastic model couples bubble and the lateral solids mixing curve comparison figure of CFD-DEM.
Fig. 6 (b) is before and after stochastic model couples bubble and the axial solids mixing curve comparison figure of CFD-DEM.
Detailed description of the invention
Below in conjunction with the accompanying drawings and specific embodiment, it is further elucidated with the present invention, it should be understood that these examples are merely to illustrate this
Invention rather than limit the scope of the present invention, after having read the present invention, various to the present invention of those skilled in the art
The amendment of the equivalent form of value all falls within the application claims limited range.
A kind of bubbling fluidized bed modeling method based on bubble and granule random motion, comprises the following steps:
Step 1, by bubbling fluidized bed grid division, the analog result of statistics early stage CFD-DEM model obtains distribution of particles
Figure.Calculate through some time step, granule transition probability between grid, set up granule phase according to transition probability
Markov chain stochastic model.Particle position information is obtained by Markov chain stochastic model.
The method for building up of Markov chain stochastic model described in described step 1: the transition probability structure between any two grid
Becoming the Markov chain transition probability matrix that this time step granule moves, in timing statistics section, all transition probability matrixs is flat
Average is as the final transition probability matrix of granule Markov process.It is calculated granule grid by transition probability matrix to believe
Breath, obtains particle position information by granule gridding information.Granule is uniformly random distribution in grid.
Step 2, the distribution of particles figure obtained time step each in timing statistics section by CFD-DEM modeling is entered
Row image recognition, the generation adding up bubble, the rule moved and grow up, set up the random progressions model of bubble, random according to bubble
Progressions model determines that bubble phase is to position.
The method for building up of the random progressions model of bubble in described step 2: statistics differing heights bubble barycenter level respectively
Position and the probability distribution of equivalent diameter, probability distribution accordingly, utilize the monte carlo method of the random number that computer produces to carry out mould
Intend the generation of bubble in bubbling fluidized bed, moving and growing up obtains the random progressions model of bubble.
The rate of climb of bubble is calculated by empirical equation；The total number of bubble keeps constant in bed, the total number of bubble by
In the bed of CFD-DEM modeling, average bubble number determines, when a bubble barycenter is increased beyond bed average height, and one
New bubble i.e. produces bottom bed.Bubble constantly rises in evolution, grows up.
Step 3, utilizes the baseball cap model of bubble shape by the Markov chain stochastic model in step 1 and step 2
The random progressions model of bubble couples, and sets up the stochastic model of bubbling fluidized bed granule motion.By step 1) granule that obtains
Positional information and step 2) bubble phase that determines substitutes into the stochastic model of bubbling fluidized bed granule motion and obtains coupling gas position
The position of granule after bubble.
The baseball cap model of bubble shape in described step 3: as it is shown in figure 1, the main body of bubble is radius is rtCircle C1 quilt
Remainder after the round C2 intercepting of equal size, including three parts, respectively first area I, second area II and the
Three region III, the 3rd region III be circle C2 intercept fall part, second area II be circle C2 intercept fall part in circle C2 on
Arc and this arc two-end-point respectively with center of circle C1 line area defined, first area I for circle the remaining arc of C1 and
The two-end-point of this arc respectively with center of circle C1 line area defined.
Be in the granule in three kinds of regions and bubble generation coupling before coupling, be respectively bubble top, bubble bottom and
Bubble trailing vortex.
Three kinds of regions particulate and bubble coupling algorithm meet the granule characteristics of motion near the bubble that Davison model describes.
Therefore the granule characteristics of motion near the bubble that Davison model describes can be used to calculate the coupling of three kinds of regions particulate and bubble
Close.
Below in conjunction with specific embodiment, the present invention will be further explained.
Embodiment describes with two dimension bubbling fluidized bed situation, and three-dimensional case can be by that analogy:
(1) first by two dimension bubbling fluidized bed grid division, the analog result of statistics early stage CFD-DEM, calculate through certain
During one time step, granule transition probability between grid, the transition probability between any two grid constitutes this time step
The Markov chain transition probability matrix of granule motion, in timing statistics section, the meansigma methods of all transition probability matrixs is as granule
The transition probability matrix that Markov process is final.After being calculated granule gridding information by transition probability matrix, granule is at net
Uniformly random distribution in lattice.
(2) the bubbling fluidized bed distribution of particles figure of each time step CFD-DEM simulation in timing statistics section is carried out figure
As identifying, statistics differing heights bubble barycenter horizontal level and the probability distribution of equivalent diameter respectively, as shown in Figure 2,3, 4.
It is distributed accordingly, utilizes computer to produce random number, judge the generation of bubble, motion in bubbling fluidized bed according to monte carlo method
And grow up.Bubble produces position by random number r0Calculate with formula (1):
Wherein, r0Representing random number, (a b) represents that computer produces a random number between a to b, w to random0Represent root
According to random number r0Bottom the bubbling bed calculated, bubble produces the abscissa of position, and f (w) represents at bubbling bed bottom transverse coordinate w
Producing the probability of bubble, w represents that bubble produces the abscissa of position bottom bubbling bed.
The rate of climb of bubble is calculated by empirical equation (2), (3)；
ht+1=ht+Δt·ut (3)
Wherein, utRepresenting t bobble rise velocity, g represents acceleration of gravity, dtRepresent that t bubble homalographic circle is straight
Footpath, htRepresenting t bubble height of center of mass, Δ t represents a time step.
The total number of bubble keeps constant in bed, CFD-DEM in the bed simulated, average bubble number determines, when a bubble
When barycenter is increased beyond bed average height, a new bubble i.e. produces bottom bed；Bubble constantly rising in evolution,
Growing up, bubble barycenter horizontal level is calculated by formula (4):
wt+1=random (w(t+1),1,wt+1,2) (4)
Wherein, wt+1Represent t+1 moment bubble barycenter abscissa, w(t+1),1Under the conditions of representing t+1 moment known bubble height
The bubble barycenter minimum abscissa calculated according to Fig. 3, wt+1,2According to Fig. 3 meter under the conditions of expression t+1 moment known bubble height
The bubble barycenter maximum abscissa calculated.
Air Bubble Size is calculated by formula (5):
dt+1=random (maximum (dt+1,5,dt+1,4,dt),dt+1,3) (5)
Wherein, dt+1Represent the face circular diameters such as t+1 moment bubble, dt+1,5Represent root under the conditions of t+1 moment known bubble height
The bubble homalographic circular diameter minima calculated according to Fig. 4, dt+1,4According to Fig. 4 meter under the conditions of expression t+1 moment known bubble height
The bubble homalographic circular diameter minima calculated, dtRepresent t bubble homalographic circular diameter, dt+1,3Represent t+1 moment known gas
The bubble homalographic circular diameter maximum calculated according to Fig. 4 under the conditions of bubble height.
(3) the baseball cap model of bubble shape is set up, as shown in Figure 1.The main body of bubble is that circle C1 is by the circle of equal size
Remainder after C2 intercepting.Being divided into white portion I and gray area II, the particle position before coupling calculates according to step (1),
Representing by hollow dots, the particle position solid dot after coupling represents.In before coupling, granule location is bubble
Region I or region II, or it is in the region III of bubble trailing vortex part, the position of granule after judging to couple.Three kinds of districts
Territory granule and bubble coupling algorithm meet the granule characteristics of motion near the bubble that Davison model describes, specifically according to formula
(6), (7), (8) calculate.
D′I=rt+random(0,1)·(rt-DI)2/rt (6)
D′II=rt-random(0,1)·(rt-DII)2/rt (7)
D′III=rt+random(0,1)·(rt-DIII)2/rt (8)
Wherein, D 'IRepresent the distance with the C1 center of circle, r after granule couples bubble in the I of regiontRepresent circle C1 and the half of circle C2
Footpath, DIRepresent the distance with the C1 center of circle, D ' before granule couples bubble in the I of regionIIRepresent in the II of region after granule coupling bubble with
The distance in the C1 center of circle, DIIRepresent the distance with the C1 center of circle, D ' before granule couples bubble in the II of regionIIIRepresent granule in the III of region
With the distance in the C2 center of circle, D after coupling bubbleIIIRepresent the distance with the C2 center of circle before granule couples bubble in the III of region.
The present embodiment is from the simulation of 15-20s, and CFD-DEM needs to expend about 150 hours, the Markov of pure granule phase with
Machine process needs about 100 minutes, also merely add about 25 minutes after coupling bubble phase, so comparing CFD-DEM, application is originally
Invention makes to calculate speed and improves about 70 times.Fig. 5 (a) and Fig. 5 (b) is that the instantaneous particle distribution before and after coupling bubble phase is right
Ratio, after bubble and granule are moved and be coupled by the application present invention intuitively, analog result has successfully reappeared the configuration of bubble
And evolution, significantly improve the feature of even particle distribution.What Fig. 6 (a) and Fig. 6 (b) was quantitative compares stochastic model
Before and after coupling bubble and the radial and axial Mixing Curve of bubbling fluidized bed granule of CFD-DEM simulation, after the application present invention,
The Markov process of grain is successfully introduced into the impact that it is moved by bubble, has significantly improved what granule Mixing Curve excessively smoothed
Shortcoming, substantially increases the precision of stochastic model.
The above is only the preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill people of the art
For Yuan, under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (8)
1. a bubbling fluidized bed modeling method based on bubble and granule random motion, it is characterised in that comprise the following steps:
Step 1, by bubbling fluidized bed grid division, the analog result of statistics early stage CFD-DEM model obtains distribution of particles figure；Meter
Calculate granule transition probability between grid, set up the Markov chain stochastic model of granule phase according to transition probability；Pass through Markov
Chain stochastic model obtains particle position information；
Step 2, the distribution of particles figure obtaining CFD-DEM modeling carries out image recognition, the statistics generation of bubble, motion and
The rule grown up, sets up the random progressions model of bubble, determines that bubble phase is to position according to the random progressions model of bubble；
Step 3, utilizes the baseball cap model of bubble shape by the Markov chain stochastic model in step 1 and the bubble in step 2
Random progressions model couples, and sets up the stochastic model of bubbling fluidized bed granule motion；By step 1) particle position that obtains
Information and step 2) position substitutes into after the stochastic model of bubbling fluidized bed granule motion obtains coupling bubble by the bubble phase that determines
The position of granule.
Bubbling fluidized bed modeling method based on bubble and granule random motion the most according to claim 1, it is characterised in that:
The method for building up of Markov chain stochastic model described in described step 1, builds according to granule transition probability between grid
The Markov chain transition probability matrix of granule motion；It is calculated granule gridding information, by this by transition probability matrix
Grain gridding information obtains particle position information.
Bubbling fluidized bed modeling method based on bubble and granule random motion the most according to claim 1, it is characterised in that:
The method for building up of the random progressions model of bubble in described step 2: statistics differing heights bubble barycenter horizontal level respectively
And the probability distribution of equivalent diameter, probability distribution utilizes random number to simulate the generation of bubble, motion in bubbling fluidized bed accordingly
And grow up and obtain the random progressions model of bubble.
Bubbling fluidized bed modeling method based on bubble and granule random motion the most according to claim 2, it is characterised in that:
The total number of bubble that described step 2 obtains in the random progressions model of bubble keeps constant in bed, the total number of bubble by
In the bed of CFD-DEM modeling, average bubble number determines, when a bubble barycenter is increased beyond bed average height, and one
New bubble i.e. produces bottom bed；Bubble constantly rises in evolution, grows up.
Bubbling fluidized bed modeling method based on bubble and granule random motion the most according to claim 1, it is characterised in that:
Granule is uniformly random distribution in grid.
Bubbling fluidized bed modeling method based on bubble and granule random motion the most according to claim 1, it is characterised in that:
The baseball cap model of bubble shape in described step 3: the main body of bubble be radius be rtCircle C1 is cut by the round C2 of equal size
Remainder after taking, including three parts, respectively first area I, second area II and the 3rd region III, the 3rd district
Territory III is that circle C2 intercepts the part of falling, and second area II is the arc and the two of this arc that circle C2 intercepts in the part fallen on circle C2
End points respectively with center of circle C1 line area defined, first area I be the two-end-point of the circle remaining arc of C1 and this arc respectively
With center of circle C1 line area defined.
Bubbling fluidized bed modeling method based on bubble and granule random motion the most according to claim 6, it is characterised in that:
It is in granule and the bubble generation coupling in three kinds of regions before coupling, is bubble top, bubble bottom and bubble respectively
Trailing vortex.
Bubbling fluidized bed modeling method based on bubble and granule random motion the most according to claim 6, it is characterised in that:
The granule characteristics of motion near the bubble that Davison model describes is used to calculate coupling of three kinds of regions particulate and bubble.
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| CN108687683A (en) * | 2018-06-04 | 2018-10-23 | 湘潭大学 | A kind of grinding wheel discrete element modeling method considering abrasive grain shape and its distribution randomness |
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| CN110516366A (en) * | 2019-08-28 | 2019-11-29 | 北京工业大学 | A kind of modeling method based on random bead micro-mixer in ultra performance liquid chromatography analysis |
| US11640145B2 (en) | 2019-11-01 | 2023-05-02 | Zhejiang University Of Technology | Establishment of location correction system for processing seafood transportation displaced by wind waves and anti-accumulation drying processing method |
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| CN108687683A (en) * | 2018-06-04 | 2018-10-23 | 湘潭大学 | A kind of grinding wheel discrete element modeling method considering abrasive grain shape and its distribution randomness |
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| CN109806734A (en) * | 2019-01-28 | 2019-05-28 | 西安理工大学 | The dynamic regulation method of desulfurizing agent distributing homogeneity in open ocean fluidized bed at elevated |
| CN109806734B (en) * | 2019-01-28 | 2021-09-10 | 西安理工大学 | Dynamic regulation and control method for distribution uniformity of desulfurizer in fluidized bed under ocean working condition |
| CN109902760A (en) * | 2019-03-18 | 2019-06-18 | 中国石油大学(北京) | Two-Dimensional Bubble recognition methods in a kind of gas-solid bubbling bed |
| CN109948694A (en) * | 2019-03-18 | 2019-06-28 | 中国石油大学(北京) | Three-dimensional bubble recognition methods in a kind of gas-solid bubbling bed based on distance restraint algorithm |
| CN109902760B (en) * | 2019-03-18 | 2020-10-27 | 中国石油大学(北京) | Two-dimensional bubble identification method in gas-solid bubbling bed |
| CN109948694B (en) * | 2019-03-18 | 2020-12-22 | 中国石油大学(北京) | Gas-solid bubbling bed three-dimensional bubble identification method based on distance constraint algorithm |
| CN110516366A (en) * | 2019-08-28 | 2019-11-29 | 北京工业大学 | A kind of modeling method based on random bead micro-mixer in ultra performance liquid chromatography analysis |
| CN110516366B (en) * | 2019-08-28 | 2023-04-07 | 北京工业大学 | Modeling method based on random microbead micromixer in ultra-high performance liquid chromatography analysis |
| US11640145B2 (en) | 2019-11-01 | 2023-05-02 | Zhejiang University Of Technology | Establishment of location correction system for processing seafood transportation displaced by wind waves and anti-accumulation drying processing method |
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Application publication date: 20161012 |