CN106980710A - ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method - Google Patents

ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method Download PDF

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CN106980710A
CN106980710A CN201710111477.0A CN201710111477A CN106980710A CN 106980710 A CN106980710 A CN 106980710A CN 201710111477 A CN201710111477 A CN 201710111477A CN 106980710 A CN106980710 A CN 106980710A
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magnetic induction
esp
field
contribution rate
induction intensity
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张建平
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Shanghai University of Electric Power
University of Shanghai for Science and Technology
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Shanghai University of Electric Power
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

Abstract

The present invention relates to a kind of ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method, including：Set up mathematical modeling and simplified model that ESP flow fields, electromagnetic field and particle aerodynamic field intercouple, utilize the efficiency of dust collection and its contribution rate of PM2.5 under the different operating modes of FLUENT Software Numerical Simulations, it is fitted using cubic polynomial function pair operating voltage contribution rate with the change curve of magnetic induction intensity, so as to improve spool formula ESP trapping performances.Compared with prior art, the present invention has the advantages that fitting precision is high.

Description

ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method
Technical field
The present invention relates to a kind of line tubular electrostatic precipitator (Electrostatic Precipitators, ESP) work electricity Contribution rate and magnetic induction intensity curve matching side are pressed, is contributed more particularly, to a kind of ESP operating voltages based on cubic polynomial Rate and magnetic induction intensity curve-fitting method.
Background technology
Haze has turned into the object that world community is paid close attention at present, and its main component is PM2.5.Thermal power plant is big How one of PM2.5 important emission source in gas, line tubular electrostatic precipitator carries as the most frequently used cleaner in coal-burning power plant High spool formula ESP turns into current important topic urgently to be resolved hurrily to the trapping performance of fine particulates.Magnetic control technology is that currently have One of new technique of effect optimization electrostatic precipitator trapping performance, control Charged movement locus is reached by externally-applied magnetic field Purpose.This method is actually rare at present, but gathers around and hold out broad prospects.
The content of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide a kind of ESP operating voltages tribute Offer rate and magnetic induction intensity curve-fitting method.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method, including：Set up ESP flow fields, electromagnetic field The mathematical modeling and simplified model intercoupled with particle aerodynamic field, using under the different operating modes of FLUENT Software Numerical Simulations PM2.5 efficiency of dust collection and its contribution rate, utilizes change of the cubic polynomial function pair operating voltage contribution rate with magnetic induction intensity Change curve to be fitted, so as to improve spool formula ESP trapping performances.
It is described to set up the mathematical modeling that flow field, electromagnetic field and particle aerodynamic field intercouple and be specially：
1) electromagnetic field
Electromagnetic field is made up of electrostatic field and externally-applied magnetic field in spool formula ESP, when there is ion and Charged in electric field During space charge, the circular cylindrical coordinate form for the Poisson's equation that potential is met can be write as：
In formula, U is away from the potential at corona wire r, V in space；R be away from space a little arrive corona wire radial distance, m；ε0For permittivity of vacuum, 8.854 × 10-12F/m；ρ is space charge density, C/m3；
Electric-field intensity E is negative rate of change of the potential with locus, i.e.,With reference to expressionWith space charge density expression formulaEquation (1) is solved to obtain：
In formula, E is electric-field intensity, V/m；I is the electric current on unit corona wire, A/m；beffFor having for space charge carrier Imitate mobility；C is integral constant；
2) flow field
In view of this incompressible condition of flue gas in two-dimentional ESP models, smoke density can be taken as constant, and consider by Broad sense source item in Navier-Stokes equations is substituted with aerodynamics drag and electric body force sum, the conservation of mass Equation and momentum conservation equation are expressed as：
In formula, ρgIt is the density of air, kg/m3；uiAnd ujFor gas velocity, m/s；Subscript " i " and " j " represent gas respectively Body is parallel and perpendicular to the direction of dust collector pole；μ is aerodynamic force viscosity, kg/ (ms)；μtIt is for turbulent kinetic viscosity Number, kg/ (ms)；P is gas average static pressure, Pa；FDjFor particle drag；
3) particle aerodynamic field
FLUENT softwares pass through to acting on the integration of the equilibrium equation on particle in two dimensional surface come to particle aerodynamic field Numerical solution is carried out, the inertia force that the equilibrium equation formula can be expressed as particle is equal to each power sum acted on particle, Expression is as follows：
In formula, mpFor the quality of particulate matter, kg；up,jRepresent particle in the speed in j directions, m/s；Lorentz force Fm,j= Qup,jB, N, wherein, Q is the carrying capacity of particle, and C, B is additional magnetic induction intensity, T；Electric field force Fe,j=QEj, N.
The described simplified model for setting up ESP is specially：
1) structural parameters of spool formula ESP simplified two-dimensional model are specially：Dust collector pole length of tube L=7.6m, corona wire Radius rw(tube)=1.0mm, dust collecting pole plate internal diameter R=0.3m；Flue gas is uniformly distributed in electric field entrance, and vertical portals are to upstream It is dynamic, if r axles be gas in extreme direction of gathering dust, Z axis is gas parallel to extreme direction of gathering dust, it is therefore assumed that dust concentration with Keep constant in concentric circumferences centered on axis；
2) using Gambit softwares to step 1) in simplified model mesh generation, 34850 grid cells are divided into altogether.
PM2.5 efficiency of dust collection and its contribution rate is specially under the described different operating modes of simulation：
Magnetic field is introduced in selected flue gas flow rate v=1.0m/s operating mode, online tubular type ESP, by changing operating voltage Size analyzes influence of the magnetic induction intensity to PM2.5 efficiency of dust collections, obtains following rule：
1) under same operating voltage, with the increase of additional magnetic induction intensity, PM2.5 efficiency of dust collection becoming in increase Gesture；
2) in same magnetic field environment, with the increase of operating voltage, PM2.5 efficiency of dust collection constantly increases, but amplification Constantly reduce, this explanation operating voltage is bigger, and the efficiency of dust collection of particle is higher, but its contribution is constantly being reduced；
3) increase with the constant amplitude of additional magnetic induction intensity, the difference of adjacent two curves constantly reduces, shown with magnetic The increase of induction, the contribution that magnetic field is trapped to PM2.5 is less and less；
4) rate of change of PM2.5 efficiency of dust collections when evaluation work voltage often improves 10kV, it can thus be concluded that existing to operating voltage The curve that the contribution λ of its efficiency of dust collection changes with magnetic induction density B during 40kV and 50kV, can be learnt by curve：No matter work Make the size of voltage, with the increase of additional magnetic induction intensity, the contribution rate of operating voltage is in downward trend；In same magnetic Under induction, operating voltage is smaller, and the contribution rate that it is trapped to PM2.5 is bigger.
Described is intended using cubic polynomial function pair operating voltage contribution rate with the change curve of magnetic induction intensity Conjunction is specially：
It is distributed if operating voltage contribution λ is satisfied by following cubic polynomial with the change curve of magnetic induction density B：
λ (B)=p1B3+p2B2+p3B+p4
In formula, p1、p2、p3、p4For the parameter to be estimated of cubic polynomial function.
Compared with prior art, the present invention utilizes cubic polynomial function pair operating voltage contribution rate with magnetic induction intensity Change curve is fitted, and has obtained analytic formula, and it is verified, shows that the approximating method precision is higher, outside Plus magnetic field can effectively improve the efficiency of dust collection of particle, this result is to traditional wire tubular type ESP scrap builds work related to dedusting The technological innovation in industry field has certain reference.
Brief description of the drawings
Fig. 1 is that externally-applied magnetic field acts on offline tubular type ESP simplified two-dimensional models and electrostatic precipitation mechanism analysis schematic diagram；
Fig. 2 is spool formula ESP mesh generation figures；
Fig. 3 is change curve of the PM2.5 efficiency of dust collections under different operating voltage with magnetic induction intensity；
Fig. 4 is change curve of the operating voltage contribution rate with magnetic induction intensity；
Fig. 5 is delta data and matched curve figure of the operating voltage contribution rate with magnetic induction intensity.
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 is described, it is clear that described embodiment is a part of embodiment of the present invention, rather than whole embodiments.Based on this hair Embodiment in bright, the every other reality that those of ordinary skill in the art are obtained on the premise of creative work is not made Example is applied, should all belong to the scope of protection of the invention.
In order to study the lower operating voltage of externally-applied magnetic field effect to line tubular electrostatic precipitator (ElectrostaticPrecipitators, ESP) traps the influence of performance, establishes flow field, electromagnetic field and particle aerodynamic field The mathematical modeling intercoupled, PM2.5 efficiency of dust collection and its contribution under different operating modes using FLUENT Software Numerical Simulations Rate, analysis has obtained following changing rule：In online tubular type ESP, with the increase of magnetic induction intensity, PM2.5 efficiency of dust collection In the trend of increase, contribution of the operating voltage to PM2.5 efficiency of dust collections is gradually reduced.In addition, utilizing cubic polynomial function pair Operating voltage contribution rate is fitted with the change curve of magnetic induction intensity, has obtained analytic formula, and it is tested Card, shows that the approximating method precision is higher.Externally-applied magnetic field can effectively improve the efficiency of dust collection of particle, and this result is to traditional wire Tubular type ESP scrap builds and the technological innovation of dedusting related industrial fields have certain reference.
1 magnetic field Analysis on Mechanism
Fig. 1 gives externally-applied magnetic field and acts on offline tubular type ESP simplified two-dimensional models and electrostatic precipitation mechanism analysis schematic diagram. Apply the inside magnetic induction intensity of paper vertical with the direction of electrostatic dust remover electric field in two-dimensional electrostatic deduster.In corona wire Dust collector pole is pointed in upper application negative high voltage, the direction of electric field force, at this moment free electron into dust collector pole motion process with grit phase Touch, and being attached on dust granules makes its bear electric, charged particle towards extreme direction of gathering dust by electric field force effect due to being done parabolic Line is moved.Introduce behind magnetic field, powered dust granules are due to, extension for the helical movement by electric field force and Lorentz force synergy Electrically charged particle residence time in ESP, change the collision course of electrically charged particle and dust collector pole, will cause the particulate matter to be more easy to be received Dirt pole is captured.
2 theoretical models
2.1 electromagnetic field
Electromagnetic field is made up of electrostatic field and externally-applied magnetic field in spool formula ESP.When there is ion and Charged in electric field During space charge, the circular cylindrical coordinate form for the Poisson's equation that potential is met can be write as：
In formula, U is away from the potential at corona wire r, V in space；R be away from space a little arrive corona wire radial distance, m；ε0For permittivity of vacuum, 8.854 × 10-12F/m；ρ is space charge density, C/m3。
Electric-field intensity E is negative rate of change of the potential with locus, i.e.,With reference to expressionWith space charge density expression formulaEquation (1) is solved to obtain：
In formula, E is electric-field intensity, V/m；I is the electric current on unit corona wire, A/m；beffFor having for space charge carrier Imitate mobility；C is integral constant.
Except electric field, there is also around moving charge in magnetic field.The magnetic field given in the present invention is equal in ESP spaces Even distribution and do not change over time, its size and Orientation is constant, be not related to maxwell equation group solution calculate.Outside Plus magnetic field causes charged particle to produce Lorentz force, is loaded into the dynamic control equation of particle.
2.2 flow field
In view of this incompressible condition of flue gas in two-dimentional ESP models, smoke density can be taken as constant, and consider by Broad sense source item in Navier-Stokes equations is substituted with aerodynamics drag and electric body force sum, the conservation of mass Equation and momentum conservation equation can
It is expressed as：
In formula, ρgIt is the density of air, kg/m3；uiAnd ujFor gas velocity, m/s；Subscript " i " and " j " represent gas respectively Body is parallel and perpendicular to the direction of dust collector pole；μ is aerodynamic force viscosity, kg/ (ms)；μtIt is for turbulent kinetic viscosity Number, kg/ (ms)；P is gas average static pressure, Pa；FDjFor particle drag.
2.3 particle aerodynamic fields
FLUENT softwares pass through to acting on the integration of the equilibrium equation on particle in two dimensional surface come to particle aerodynamic field Numerical solution is carried out, the inertia force that the equilibrium equation formula can be expressed as particle is equal to each power sum acted on particle, Expression is as follows：
In formula, mpFor the quality of particulate matter, kg；up,jRepresent particle in the speed in j directions, m/s；Lorentz force Fm,j= Qup,jB, N, wherein, Q is the carrying capacity of particle, and C, B is additional magnetic induction intensity, T；Electric field force Fe,j=QEj, N.
The solution procedure of 3 application software
3.1 physical model
Spool formula ESP simplified two-dimensional model is as shown in figure 1, structural parameters are specially：Dust collector pole length of tube L=7.6m, Corona wire radius rw(tube)=1.0mm, dust collecting pole plate internal diameter R=0.3m.Flue gas is uniformly distributed in electric field entrance, vertical portals to Upper flowing, if r axles be gas in extreme direction of gathering dust, Z axis be gas parallel to extreme direction of gathering dust, it can thus be assumed that dust Concentration keeps constant in the concentric circumferences centered on axis.
3.2 mesh generation
Using Gambit softwares to the simplified model mesh generation shown in Fig. 1,34850 grid cells are divided into altogether, such as Shown in Fig. 2.
Influence of the operating voltage to efficiency of dust collection under 4 magnetic field environments
Magnetic field is introduced in selected flue gas flow rate v=1.0m/s operating mode, online tubular type ESP, by changing operating voltage Size analyzes influence of the magnetic induction intensity to PM2.5 efficiency of dust collections, as shown in Figure 3.By Fig. 3 it can be found that：
1) under same operating voltage, with the increase of additional magnetic induction intensity, PM2.5 efficiency of dust collection becoming in increase Gesture；
2) in same magnetic field environment, with the increase of operating voltage, PM2.5 efficiency of dust collection constantly increases, but amplification Constantly reduce, this illustrates that operating voltage is bigger, and the efficiency of dust collection of particle is higher, but its contribution is constantly being reduced；
3) increase with the constant amplitude of additional magnetic induction intensity, the difference of adjacent two curves constantly reduces, indicate with The increase of magnetic induction intensity, the contribution that magnetic field is trapped to PM2.5 is less and less.
With reference to the curve in Fig. 3, can evaluation work voltage PM2.5 efficiency of dust collections when often improving 10kV rate of change, thus It can obtain the curve that the contribution λ of operating voltage its efficiency of dust collection in 40kV and 50kV changes with magnetic induction density B, such as Fig. 4 It is shown.It can be seen that：No matter the size of operating voltage, with the increase of additional magnetic induction intensity, the contribution rate of operating voltage is equal In downward trend；Under same magnetic induction intensity, operating voltage is smaller, and the contribution rate that it is trapped to PM2.5 is bigger.
5 are carried out curve fitting using cubic polynomial to ESP operating voltages contribution rate-magnetic induction intensity
Analytical conclusions can carry for novel magnetic controlled dedusting technology on operating voltage, the optimization design of magnetic induction intensity in Fig. 4 For technical parameter, for the ease of engineering design application, operating voltage contribution rate is provided by curve matching here strong with magnetic induction Spend the analytic formula of change.Approximating method is provided with reference to the data point in Fig. 4, and using example to the accurate of matched curve Degree is verified.
It is distributed if operating voltage contribution λ is satisfied by following cubic polynomial with the change curve of magnetic induction density B：
λ (B)=p1B3+p2B2+p3B+p4 (6)
In formula, p1、p2、p3、p4For the parameter to be estimated of cubic polynomial function.With reference to operating voltage in Fig. 4 in 40kV and The data (except B=0.25T) that its contribution rate changes with magnetic induction intensity during 50kV, using least square method, can be obtained respectively To 40kV and 50kV fitting formula, that is, have：
λ(B)40kV=-63.6B3+62.12B2-33.755B+12.35 (7)
λ(B)50kV=-26.42B3+31.56B2-16.74B+5.232 (8)
Fig. 5 gives the operating voltage matched curve that its contribution rate changes with magnetic induction intensity in 40kV and 50kV, can To find out, data point and the degree of agreement of matched curve are fine under two kinds of operating voltages, and matched curve is relatively accurately described Operating voltage contribution rate is with magnetic induction intensity variation relation.In addition, the fitting coefficient of determination of two matched curves is respectively 0.9968 and 0.9982,1 is relatively close to, is had this further illustrates the formula based on cubic polynomial (7) and (8) preferable Fitting precision.
Example：
When magnetic induction intensity is B=0.25T, the limited of operating voltage contribution rate can obtain by this paper calculation procedure First calculated value (hollow dots for corresponding respectively to 40kV and 50kV in Fig. 5), respectively λ40kV=6.86 and λ50kV=2.61.By B= 0.25T is substituted into formula (7) and (8) respectively, and the match value for obtaining operating voltage contribution rate is respectivelyWithOn the basis of FEM calculation value, the fitting of its contribution rate is relative when can obtain operating voltage for 40kV and 50kV Error delta40kVAnd δ50kV, it is respectively：
As can be seen here, the theory and numerical model herein for solving ESP efficiency of dust collections under magnetic field environment are practical , there is higher precision, parsing with the change of magnetic induction intensity using cubic polynomial Function Fitting operating voltage contribution rate Formula relative error is no more than 1%, meets engineering demand.
The foregoing is only a specific embodiment of the invention, but protection scope of the present invention is not limited thereto, any Those familiar with the art the invention discloses technical scope in, various equivalent modifications can be readily occurred in or replaced Change, these modifications or substitutions should be all included within the scope of the present invention.Therefore, protection scope of the present invention should be with right It is required that protection domain be defined.

Claims (5)

1. a kind of ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method, it is characterised in that including：Set up ESP streams Mathematical modeling and simplified model that field, electromagnetic field and particle aerodynamic field intercouple, utilize FLUENT Software Numerical Simulations different PM2.5 efficiency of dust collection and its contribution rate under operating mode is strong with magnetic induction using cubic polynomial function pair operating voltage contribution rate The change curve of degree is fitted, so as to improve spool formula ESP trapping performances.
2. a kind of ESP operating voltages contribution rate according to claim 1 and magnetic induction intensity curve-fitting method, its feature It is, it is described to set up the mathematical modeling that flow field, electromagnetic field and particle aerodynamic field intercouple and be specially：
1) electromagnetic field
Electromagnetic field is made up of electrostatic field and externally-applied magnetic field in spool formula ESP, when the space that there is ion and Charged in electric field During electric charge, the circular cylindrical coordinate form for the Poisson's equation that potential is met can be write as：
d 2 U dr 2 + 1 r d U d r + ρ ϵ 0 = 0 - - - ( 1 )
In formula, U is away from the potential at corona wire r, V in space；R is away from the radial distance that corona wire is a little arrived in space, m；ε0For Permittivity of vacuum, 8.854 × 10-12F/m；ρ is space charge density, C/m3；
Electric-field intensity E is negative rate of change of the potential with locus, i.e.,With reference to expression With space charge density expression formulaEquation (1) is solved to obtain：
E = - I 2 πb e f f ϵ 0 + C 2 r 2 - - - ( 2 )
In formula, E is electric-field intensity, V/m；I is the electric current on unit corona wire, A/m；beffFor effectively moving for space charge carrier Shifting rate；C is integral constant；
2) flow field
In view of this incompressible condition of flue gas in two-dimentional ESP models, smoke density can be taken as constant, and consider by Broad sense source item in Navier-Stokes equations is substituted with aerodynamics drag and electric body force sum, the conservation of mass Equation and momentum conservation equation are expressed as：
∂ ∂ x i ( ρ g u i ) = 0 - - - ( 3 )
ρ g ∂ ∂ t ( u j ) + ∂ ∂ x i ( ρ g u j u i ) = - ∂ P ∂ x j + ( μ + μ t ) ∂ 2 u j ∂ x i 2 + F D j + ρE j - - - - ( 4 )
In formula, ρgIt is the density of air, kg/m3；uiAnd ujFor gas velocity, m/s；It is parallel that subscript " i " represents gas respectively with " j " With perpendicular to the direction of dust collector pole；μ is aerodynamic force viscosity, kg/ (ms)；μtFor turbulent kinetic viscosity, kg/ (m·s)；P is gas average static pressure, Pa；FDjFor particle drag；
3) particle aerodynamic field
FLUENT softwares to acting on the integration of the equilibrium equation on particle in two dimensional surface to particle aerodynamic field by carrying out Numerical solution, the inertia force that the equilibrium equation formula can be expressed as particle is equal to each power sum acted on particle, specifically Expression formula is as follows：
m p du p , j d t = F m , j + F e , j + F D , j - - - ( 5 )
In formula, mpFor the quality of particulate matter, kg；up,jRepresent particle in the speed in j directions, m/s；Lorentz force Fm,j=Qup,jB, N, wherein, Q is the carrying capacity of particle, and C, B is additional magnetic induction intensity, T；Electric field force Fe,j=QEj, N.
3. a kind of ESP operating voltages contribution rate according to claim 1 and magnetic induction intensity curve-fitting method, its feature It is, the described simplified model for setting up ESP is specially：
1) structural parameters of spool formula ESP simplified two-dimensional model are specially：Dust collector pole length of tube L=7.6m, corona wire radius rw(tube)=1.0mm, dust collecting pole plate internal diameter R=0.3m；Flue gas is uniformly distributed in electric field entrance, and vertical portals are flowed up, if r Axle be gas in extreme direction of gathering dust, Z axis is gas parallel to extreme direction of gathering dust, it is therefore assumed that dust concentration using axis as Keep constant in the concentric circumferences at center；
2) using Gambit softwares to step 1) in simplified model mesh generation, 34850 grid cells are divided into altogether.
4. a kind of ESP operating voltages contribution rate according to claim 1 and magnetic induction intensity curve-fitting method, its feature It is, PM2.5 efficiency of dust collection and its contribution rate is specially under the described different operating modes of simulation：
Magnetic field is introduced in selected flue gas flow rate v=1.0m/s operating mode, online tubular type ESP, by the size for changing operating voltage To analyze influence of the magnetic induction intensity to PM2.5 efficiency of dust collections, following rule is obtained：
1) under same operating voltage, with the increase of additional magnetic induction intensity, PM2.5 efficiency of dust collection is in the trend increased；
2) in same magnetic field environment, with the increase of operating voltage, PM2.5 efficiency of dust collection constantly increases, but amplification is continuous Reduce, this explanation operating voltage is bigger, and the efficiency of dust collection of particle is higher, but its contribution is constantly being reduced；
3) increase with the constant amplitude of additional magnetic induction intensity, the difference of adjacent two curves constantly reduces, shown with magnetic induction The increase of intensity, the contribution that magnetic field is trapped to PM2.5 is less and less；
4) rate of change of PM2.5 efficiency of dust collections when evaluation work voltage often improves 10kV, it can thus be concluded that to operating voltage in 40kV The curve that the contribution λ of its efficiency of dust collection changes with magnetic induction density B during with 50kV, can be learnt by curve：No matter work electricity The size of pressure, with the increase of additional magnetic induction intensity, the contribution rate of operating voltage is in downward trend；In same magnetic induction Under intensity, operating voltage is smaller, and the contribution rate that it is trapped to PM2.5 is bigger.
5. a kind of ESP operating voltages contribution rate according to claim 1 and magnetic induction intensity curve-fitting method, its feature It is, described utilization cubic polynomial function pair operating voltage contribution rate is fitted tool with the change curve of magnetic induction intensity Body is：
It is distributed if operating voltage contribution λ is satisfied by following cubic polynomial with the change curve of magnetic induction density B：
λ (B)=p1B3+p2B2+p3B+p4 (6)
In formula, p1、p2、p3、p4For the parameter to be estimated of cubic polynomial function.
CN201710111477.0A 2017-02-28 2017-02-28 ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method Pending CN106980710A (en)

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