CN107664628A - It is a kind of predicting the method for atmospheric visibility - Google Patents
It is a kind of predicting the method for atmospheric visibility Download PDFInfo
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Abstract
It is a kind of predicting the method for atmospheric visibility.The invention discloses the method that coupling Taylor expansion Moment Methods and Mie scattering theory fitting of a polynomials realize atmospheric visibility prediction.The present invention discloses Taylor expansion Moment Methods expansion exponent number, basic function expression formula, and the selection principle of Mie scattering theory fitting of a polynomial exponent numbers.Technical solution of the present invention provides technological means for the prediction of indoor and outdoors atmospheric visibility.
Description
Technical field
The present invention relates to atmospheric environment technical field, and in particular to atmospheric aerosol, Atmospheric particulates environmental monitoring and survey
Amount.
Background technology
When light passes through aerosol, particulate can be interacted with light, and scattering and sink effect are produced to light, this
The resultant effect of two effects is referred to as the extinction effect of particulate.Extinction coefficient is the quantization means of particle extinction effect,
Using the overall extinction coefficient of numerical calculations aerosol, the development to optical particle counter, and aerosol visibility
Numerical simulation, it is all significant.
Scattering of the particle to light wave, if only considering the situation that light wave frequency before and after scattering does not change, then root
According to the difference of particle size, Rayleigh scattering, Mie scattering and geometric optics scattering can be divided into.When the yardstick of particle is much smaller than incidence
It is referred to as Rayleigh scattering during optical wavelength；When particle size is much larger than lambda1-wavelength, it scatters the grain met in geometric optics
Sub- scattering theory；When particle size is close with lambda1-wavelength, the different parts of particle and the incidence wave of different piece are mutual
Effect, Rayleigh scattering are no longer applicable, and for geometric optics, the particle under the yardstick is again too small, at this moment, it is necessary to use Gustav
The Mie scattering theories that Mie is proposed, therefore the light wave scattering under the yardstick particle is referred to as Mie scattering.Mie theory are
The analytic solutions that G.Mie is derived by Maxwell ' s equation under spherical medium, theoretically, Mie theories are places
It is theoretical to Scattering of Plane Waves and the generality absorbed to manage uniform-spherical particle, particle size very little or it is very big when, Mie scattering reasons
It is consistent with the result that Rayleigh scattering and geometric optics scatter respectively by obtained result.
The overall extinction coefficient of aerosol in atmospheric environment, it is expressed as the sum of scattering coefficient and absorption coefficient, its expression formula
It is as follows：
bext=bsg+bag+bsp+bap
Wherein, bsgAnd bagIt is scattering and absorption coefficient of the gas to light wave, bspAnd bapIt is that particulate dissipates to light wave
Penetrate and absorption coefficient.
Under the atmospheric environment of cleaning, aerosol particle is less, and the mainly sky of scattering and sink effect occurs with visible ray
Molecule in gas, such as nitrogen, oxygen and carbon dioxide, Rayleigh scattering can be used theoretical.But for contaminated air
Or the aerosol environment under foggy weather, the main contributions for visible ray occurring scattering and sink effect come from aerosol particle,
Now Rayleigh scattering theory is no longer applicable, and needs to use Mie scattering theories.
The main task of numerical computations is carried out to particulate extinction coefficient, is the single-particle for calculating each yardstick respectively
Extinction coefficient, and aerosol particle are simulated with the Scaling Evolution of time.
In theory, extinction coefficient of the particle of each yardstick under specific lambda1-wavelength, the theory that can be scattered by Mie
Formula calculates (Bohren＆Huffman 1983).From Mie scattering theories, the extinction coefficient of particle depend primarily on into
Optical wavelength, the yardstick of particle and refractive index (Bohren＆Huffman 1983) are penetrated, but its theoretical formula has used complexity
Series is expressed, and these series convergences are slow, and computational efficiency is low.
Aerosol particles are with the Scaling Evolution of time, it is necessary to carry out numerical computations to particle PBE equations, conventional is subregion
Method (Gelbard et al., 1980a, 1980b), this method are the direct numerical computations to kinetics equation.It can be not pre-
First distribution of particles is developed on the premise of pre-supposing that, obtain the particle size Spectral structure of each timing node, and
After the subregion of particle size reaches certain amount, high-precision result can be obtained.It is theoretical but its shortcomings that is also evident from
On, on each timing node, each particle diameter subregion is required for solving particle PBE equations successively with other subregions, causes to calculate
Overlong time.
After above-mentioned two parts result is tried to achieve respectively, it is possible to using direct integral formula, according on each timing node
Particle size Spectral structure, particle extinction coefficient on each yardstick is integrated, that is, obtains aerosol entirety extinction effect at any time
Between evolution.However, it will be apparent that calculated using extinction coefficient direct integral formula, it is necessary to ask for extinction coefficient and particle
The substantial amounts of calculating time is spent on yardstick Spectral structure, causes it to rest on theoretical modeling, is unfavorable for being generalized to practical application
In.
For the above reasons, for the numerical computations of Aerosol Extinction, it is necessary to find one kind and have computational efficiency concurrently
With the computational methods of precision.
Research for aerosol particle, many times only needing to pay close attention to the statistical information of all particles, including gas is molten
The particle number concentrations of particle, average grain diameter, particle dispersion etc. in glue, it is exactly the square amount of particle in mathematical meaning, for so
Idea, Moment Methods are suggested (Hulburt＆Katz 1964).The great advantage of Moment Methods was to the square amount of particle with the time
Numerical computations efficiency, opposite sectors method is much higher.The Taylor expansion Moment Methods that Yu and Lin (2008) are proposed, are to square
The improvement of method, it can obtain taking into account precision in the case where in advance not pre-supposing that the size distribution in particle evolutionary process
With each rank square amount of computational efficiency.But TEMOM is applied to the calculating of Aerosol Extinction, there is presently no this respect
Work occurs.For the extinction coefficient of particle, Jung and Kim (2006,2007) are successively proposed using fitting of a polynomial and tune
With average method, quick approximate calculation is carried out to particle extinction coefficient.
In the research and practice process to the method, the inventors found that：Taylor expansion square will be used first
Method, and the polynomial fitting method that Jung and Kim is proposed is combined, Aerosol Extinction is calculated, air can be shown in
Degree is predicted.
The content of the invention
Carried to solve above-mentioned technology object for appreciation present in prior art, the invention provides one kind to predict air energy
The method of degree of opinion, this method can provide the specific targets of atmospheric visibility in the case where that need not measure.Particular content bag
Include：
(1) for Moment Methods to realize the real-time description of Atmospheric particulates dynamic evolution feature, Moment Methods use Taylor's exhibition
The technology of opening realizes the non-closing for solving square amount, i.e. Taylor expansion Moment Methods；
(2) method for using fitting of a polynomial, intends the light scattering coefficient of the particulate matter given by Mie scattering theories
Close, provide corresponding fitting expression；
(3) Taylor expansion Moment Methods are coupled and according to fitting gained expression formula, realizes the real-time estimate to atmospheric visibility.
Above-mentioned technical proposal can be seen that because the embodiment of the present invention uses Taylor expansion Moment Methods and Mie scattering theories
The method of coupling is fitted, directly gives real-time atmospheric visibility index, therefore, this method saves apparatus measures cost, prospect
It is vast.
Brief description of the drawings
Fig. 1 is that zone method and Taylor expansion Moment Methods calculate comparative result figure to square amount；
Fig. 2 is Error Graph of the Taylor expansion Moment Methods result of calculation relative to zone method；
Fig. 3 is the refractive index figure under several typical aerosol environment；
Fig. 4 is the theoretical curve and matched curve comparison diagram of Carbon particle extinction coefficients；
Fig. 5 a- Fig. 5 f are the prediction result figure (being contrasted with Mie＆SM method) to different primary condition using the present invention.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained all other under the premise of creative work is not made
Embodiment, belong to the scope of protection of the invention.
Offer of the embodiment of the present invention is a kind of to predict the method for atmospheric visibility, can not needed indoors with outdoor
In the case of measurement apparatus, visibility index is provided.It is described in detail individually below.
1) particle PBE equations
In aerosol systems, the physics such as Blang's coalescence, condensation, crystallization nucleation, diffusion, chemical process can occur for particle,
But under micro-nano-scale, Blang's coalescence process accounts for governance effect.The governance equation of these processes, is claimed in aerosol systems
For particle PBE equations.In the present invention, in order to simplify narration, only choose Blang's coalescence process and be described.So, particle PBE
Equation is expressed as follows (Friedlander 2000)：
Here, n (v, t) represents particle scale Spectral structure, i.e. during moment t, volume is the concentration (or quantity) of v particle；β
(v, v ') is that volume is respectively that the collision kernel function of coalescence occurs for v and v ' particle.
It can be seen that PBE equations are a strong nonlinearity calculus models, so far, on the basis without any hypothesis
On, corresponding, proper analytic solutions are not obtained also.With the development of computer technology and numerical value computational theory, lead to
The mode direct solution PBE equations for crossing numerical computations are possibly realized, common such as zone method.Due in strict accordance with PBE equations
Calculated, make this method in the case where subregion is more, other method is far above to the precision of particle simulation, but still deposit
Computationally intensive and efficiency is low the shortcomings that.In order to solve these problems, researcher proposes a lot of other methods, these methods
Respectively there are advantage and disadvantage, in the absence of superiority-inferiority, should be selected according to the needs of actual use.
The Taylor expansion Moment Methods that the present invention uses, solves the closed question of moment equation by Taylor expansion.
2) Blang's coalescence
The Brownian movement of particle is the main reason for Blang's coalescence process occurs.Particle Blang coalescence and Knudsen numbers
(Kn) closely related, it is defined as the ratio between the mean free path of air and particle radiusAccording to Kn numbers can
Grain is divided into free-molecule regime, transition region, nearly continuum and continuum.In free-molecule regime, the area can be obtained by theory deduction
Between particles collision kernel function：
To the particle of continuum and nearly continuum, it is as follows that it collides kernel function：
Wherein, v be particle volume, kbFor Boltzmann constant, T is gas temperature, and ρ is grain density, and μ moves for particle
Mechanics viscosity, Cc(Kn, v) is the slip correction factor, and its size is determined by Kn and particle volume v.
Blang's coalescence is that aerosol or other micro-nano granules are spontaneous, the phenomenon that is permanently present, and with particle, Blang coagulates
And the trend constantly increased can be presented in the lasting progress moved, the yardstick of particle, the size distribution for ultimately resulting in particle may
Across multiple particle scale regions including free-molecule regime, transition region, nearly continuum and continuum.In this premise
Under, the single particles collision kernel function using a certain yardstick area, it is impossible to the accurately evolution of description aerosol particle yardstick
Journey.But so far, the collision kernel function between the whole district is derived under identical theoretical frame, is still not carried out.It is at present
Only, it can only be handled on existing collision kernel functional foundations, obtain the collision kernel function between the whole district.
The present invention is pushed away collision kernel function by carrying out harmonic average to the collision kernel function of free-molecule regime and continuum
Extensively between the whole district.Handled simply, and be verified feasible to a certain extent using this method.
3) Taylor expansion Moment Methods
In a variety of method for numerical simulation to PBE, Moment Methods (Hulburt＆Katz 1964) are a kind of relatively common
Numerical computation method.Moment Methods are to obtain required various information by calculating each rank square of particle scale Spectral structure, bag
The evolution with the time such as average dispersiveness of particle number concentrations, mean particle size size, particle is included, there is higher computational efficiency
And precision.But early stage Moment Methods have the problem of equation is difficult to closing, so there are a variety of improved Moment Methods
(Pratsinis 1988；Pratsinis&Kim 1989；Friedlander 1983,2000；Frenklach 1985；
Frenklach&Harris 1987；McGraw&Tandon 2003；Yu&Lin 2008).The Taylor expansion square that the present invention uses
Method (Yu＆Lin 2008), PBE moment equation has cleverly been handled using Taylor expansion method, moment equation is closed.Together
When, Taylor expansion Moment Methods need not pre-suppose that to the size distribution in particle evolutionary process in advance, with its several need
Pre-suppose that the Moment Methods of particle distribution are compared, it has wider array of applicability.
Deformation is carried out to equation (1) first and is converted into moment equation：
Here, square mkIt is defined as：
In order that equation can calculate non-integral order square amount, to vkCarry out Taylor expansion：
Wherein, u is the central point of Taylor expansion, is defined herein as u=m1/m0。
It is continuing with formula (4) to be calculated, it is necessary to block the Taylor expansion item on the right side of formula (4), carry
The quantity that height retains item can improve precision, but the order higher calculating time also can be elongated, it is therefore desirable to according to the actual requirements, choosing
Select the quantity for retaining item., can be to meet computational efficiency and computational accuracy requirement simultaneously, therefore when expansion item remains into 3
Intercept formula (4)：
Bring formula (5) and collision kernel function into formula (2) and (3), it is possible to by Order Moments m0, m1, m2It is linear
Combination is indicated：
Thus moment equation is closed.
According to the definition of square, m0What is characterized is particle granules concentration, m1/3What is characterized is particle geometric mean diameter, m2/3Table
Sign is particle geometric average surface area, m1What is characterized is particle geometric average volume, m2What is characterized is particle dispersiveness.By Fig. 1
It can be seen that in the case of considering Blang's coalescence merely, the concentration of aerosol systems endoparticle, average grain diameter, average surface area are all in
Downward trend, and dispersiveness is then in rising trend, these are consistent with actual phenomenon.By Fig. 2 it can be seen that, relative to zone method
Numerical result, Taylor expansion Moment Methods can obtain the result of degree of precision, and especially in low-order moment, accuracy benefits are obvious.For height
Rank square, although the growth walked over time, relative error can increase, and stablize this relatively in certain time step according to it
Feature, can also suitably it be applied.
4) extinction coefficient
4.1 particle extinction coefficients
What the scattering efficiency of particle represented is particle per cross sectional in face of the energy that incident light is intercepted and captured and incident light total energy
The ratio of amount.It is similar, what the absorption efficiency of particle represented is particle per cross sectional in face of the energy that incident light is sponged with
The ratio of incident light gross energy.The energy eliminated from incident light, that is, scatter energy and absorption energy and with incident light total energy
The ratio of amount, it is referred to as particle extinction coefficient：
Qext(m, p)=Qsca(m,p)+Qabs(m,p)
Wherein, m is refractive index, and p is scale coefficient, is defined as follows：
Wherein, dpFor particle diameter, λ is lambda1-wavelength.
Previously mentioned mistake, Mie scattering can solve the extinction coefficient of any yardstick uniform-spherical particle in theory.Mie
Theory theoretical formula is in use, final only relevant with m and p.The particle extinction coefficient obtained by the theoretical calculation, works as grain
When sub- yardstick is much smaller than lambda1-wavelength (p ＜ ＜ 1), the extinction coefficient obtained with Rayleigh scattering formula coincide；Work as particle size
During much larger than lambda1-wavelength (p ＞ ＞ 1), meet geometric optics again；And when particle size is close with lambda1-wavelength (p ≈ 1)
When, the scattering efficiency of particle can only be solved by Mie scattering equation.
Fig. 3 shows the extinction coefficient of single-particle under each refractive index, and what is selected here is Hinds (1999)
The refractive index for several typical aerosols that (Garcia N í eto 2002) is defined.
As seen from Figure 3, when refractive index is without imaginary part, that is, when only existing scattering effect, real part is bigger, particle extinction coefficient with
Particle size corresponding to particle size increase crest is smaller, and vibrates more obvious；When refractive index has imaginary part, i.e., deposit simultaneously
In scattering effect and sink effect, imaginary part is bigger, and particle extinction coefficient is all the more smooth with particle size increase.These phenomenons
Caused by being due to the electromagnetic coupled of different scale particle and photon.
After single-particle extinction coefficient is obtained, with reference to the yardstick Spectral structure of particle, you can pass through integral formula directly below：
The overall extinction coefficient of aerosol systems is calculated.
Aerosol Extinction is commonly used for the visibility for calculating aerosol.The definition of visibility is, just can be experiment
The distance that object and background distinguish.The suggesting formulas provided according to Koschmieder：
Wherein, LvVisibility (m) is represented, the constant of molecule is relevant with contrast threshold, and 3.912 be accepted value.
In this manner it is possible to pass through the Aerosol Extinction b tried to achieveextTo calculate the visibility of aerosol.
4.2 polynomial fitting method
Mie theory formula form is complicated, directly can not be combined with PBE Moment Methods.In order to by Mie scattering on
The Theory Solution of particle extinction coefficient is combined with PBE Moment Methods, it is necessary to which the particle extinction coefficient that Mie theory are tried to achieve is bent
Line, high-order polynomial of one indeterminate only relevant with particle size is fitted to, i.e., to the particle extinction coefficient under specific lambda1-wavelength
Carry out fitting of a polynomial.
The characteristics of having benefited from the high computational accuracy of Taylor expansion Moment Methods, and supporting decimal rank square amount to calculate, can be appropriate
The fitting of a polynomial using higher order approach single-particle extinction coefficient curve, so as to be as a result more nearly theoretical value.Above
Mentioned, if the reservation item of increase formula (4), can improve the computational accuracy to higher order square.By to formula in the present invention
(4) 5 are retained, the maximum square amount that Taylor's Moment Methods are supported rises to 4 rank squares.In the present invention, 6 rank multinomials will be used respectively
It is fitted with 9 rank multinomials, analysis is compared to the precision of result of calculation.By taking 9 rank multinomials as an example, what is be fitted is more
Item formula is defined as follows：
Wherein, k represents the order of this, AkThe coefficient of k order items is represented, λ represents lambda1-wavelength.
Formula (8) is substituted into formula (6), you can obtain the approximate formula on Aerosol Extinction.It should be noted
It is that for the characteristic dimension that direct integral formula (6) uses for particle diameter, the present invention uses particle volume, it is necessary to enter to formula (6)
Line translation, then formula (8) is brought into and can obtain：
Here, A 'kThe coefficient of k order items is represented, is defined as
Calculated by the coupling above in relation to formula (2) and formula (9), it is possible to quickly calculate Aerosol Extinction.
Fig. 5 a-5f are using the light scattering coefficient and Mie＆SM comparing result in present invention gained air.
Claims (4)
- It is 1. a kind of predicting the method for atmospheric visibility, it is characterised in that Moment Methods are realizing Atmospheric particulates dynamics The real-time description of Characteristics of Evolution, Moment Methods realize the non-closing for solving square amount, i.e. Taylor expansion square side using Taylor expansion technology Method；Using the method for fitting of a polynomial, the light scattering coefficient of the particulate matter given by Mie scattering theories is fitted, provided Corresponding fitting expression；Couple Taylor expansion Moment Methods and according to fitting gained expression formula, realize the reality to atmospheric visibility When predict.
- It is 2. according to claim 1 predicting the method for atmospheric visibility, it is characterised in that：The Taylor expansion square side The expansion exponent number that method uses for 3, the basic function expression formula that uses for：Wherein mkK is the Order Moments amount that numerical value is more than zero, and u is Taylor expansion central point, u=m1/m0。
- 3. Mie scattering theories polynomial fitting method according to claim 1, it is characterised in that：Mie scattering theories are multinomial Formula approximating method is directed to particle scale<0.1 μm, it is fitted using 6 rank multinomials；For particle scale>It is 0.1 μm, multinomial using 9 ranks Formula is fitted.
- 4. Mie scattering theories polynomial fitting method according to claim 1, it is characterised in that：Single-particle Mie scattering reasons By the light scattering coefficient of fitting gained, during by integrating to obtain particle swarm light scattering coefficient, the square amount of appearance Closed using Taylor expansion Moment Methods.
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| 于明州 等: "湍动剪切微米尺度粒子凝并TEMOM模型研究", 《力学学报》 * |
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