Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Theoretical and experimental justification for the Schrödinger equation wikipedia, lookup

Double-slit experiment wikipedia, lookup

Canonical quantization wikipedia, lookup

Relativistic quantum mechanics wikipedia, lookup

Electron scattering wikipedia, lookup

Compact Muon Solenoid wikipedia, lookup

Elementary particle wikipedia, lookup

Identical particles wikipedia, lookup

Standard Model wikipedia, lookup

Mathematical formulation of the Standard Model wikipedia, lookup

ATLAS experiment wikipedia, lookup

Grand Unified Theory wikipedia, lookup

Future Circular Collider wikipedia, lookup

Transcript

CE 583 – The Nature of Particulate Pollutants Jeff Kuo, Ph.D., P.E. [email protected] 1 Content Primary and Secondary Particles Settling Velocities and Drag Forces Stokes’ law Stokes’ stopping distance Aerodynamic particle diameter Diffusion of particles Particle Size Distribution Functions Gaussian and log-normal By weight and by number Behavior of Particles in the Atmosphere 2 Primary and Secondary Particles ballmill Particulates make an air stream visible and hazy. Particulates are not chemically uniform (sizes, shapes, chemical compositions). Some are more harmful and visible. Not all particles are spherical (rod-like asbestos) diameter of sphere of equal volume. Micron () means micrometer (m) Ones cause significant problems: 0.01 – 10 . Particles >100 will not pass a Tyler 150 mesh screen. Most mechanical processes will not create particles < 10 (except paint pigments and ground talc). 3 Primary and Secondary Particles Most fine particles (0.1 to 10 ) are formed by combustion, evaporation or condensation. Directly above a burning tobacco is a transparent zone (gaseous HC), above it is visible smoke (condensed HC – tars, oils of 0.01 to 1 ). Smokes from tailpipe of an “oil-burning” car are all high MW hydrocarbon. Uncommon in air pollution to distinguish fine particles that are liquids or solids. Ash – incombustible materials left behind after burning (oxides of silicon, calcium, aluminum,..) 4 Primary and Secondary Particles char soot Fly ash in coal burning contain two groups: ~0.02 : contains high % of volatile materials (P, Mg, Na, K, Cl, Zn, Cr, As, Co, and Sb) – formed by condensation of vaporized materials. ~10 : those not vaporized (oxides of Si, Al, Ca,…) Coal char: porous residue (HC gases were driven off by high T) from incomplete burning. blue= N; red = O Soot: long, lacy filaments up to a few mm long. Soot is actually agglomerate of fine particles - formed in flames from vaporizing HC. Spherical metal ash particles – chars & soot were burned 5 Rain drop 6 7 Primary and Secondary Particles V D3 A D2 A 1 V D When two fine particles are brought into contact, they will stick by electrostatic and van der Waals forces. These forces are ~ area of particle (or D2) Gravity and inertial forces are ~ mass of particle (or D3) As D, D3 faster than D2 (surface forces become important). 8 Primary and Secondary Particles V D3 A D2 A 1 V D Thus, the basic strategy for particulate control is to agglomerate them into larger ones for removal forcing the contact (settling chamber, cyclone, ESP, or filters) or contact with water (scrubber). Some particulates can be formed in the atmosphere from gaseous pollutants – secondary particles (from HC, oxides of N, oxides of sulfur) vs. primary particles – emitted as particles. 9 Primary and Secondary Particles Particles efficient in scattering the light are those with D close to wavelength of light (0.4 to 0.8 ) – mostly by secondary particles. The Great Smoky Mountains National Park of Tennessee got its name from secondary particles formed from the HC emitted from the forests. Inhalable particles (< 10 ); respirable particles (< 3.5 ); fine particles (< 2.5 ) 10 Settling Velocity and Drag Forces The “terminal gravitational settling” velocity for 1-mm sand grain (1000-,SG =2) in air is 600 cm/s, and that for 1- is 0.006 cm/s. One will settle, the other won’t. Dusts (settle quickly) vs. suspendable particles – arbitrary definition: ~ 10. Aerosols – particles small enough to remain suspended in the atmosphere/gases for long times (as if they were dissolved). 11 Settling Velocity and Drag Forces – Stokes’ Law Balance between gravity and drag forces At the “terminal gravitational settling” velocity, the sum of the forces acting is zero. Can be used to determine the size of settling chambers for removing dust particles from gas or liquid streams. ( part fluid ) 2 Stokes’ law: V gD 18 Ex. 8.1: 1 micron particle 3 ( 2000 1 . 2 kg / m ) 2 6 2 V (9.81m / s )(10 m) 18(1.8 10 5 kg / m s) 6.05 10 5 m / s 1.99 10 4 fps 12 Settling Velocity and Drag Forces – Stokes’ Law Particle moving through fluid C v A F 2 D p F D Drag force, FD d v FD 3 CD = drag coefficient Ap = projected area of particle rF = density of fluid vr = relative velocity p r d v Re p =particle shape factor (=1 for sphere) r Stokes Regime Rigid spheres 10-4 < Re < 1 dp = particle diameter = fluid viscosity r 2 F 24 CD Re For large particles (0.3 Re 1000) 24 CD (1 0.14 Re 0.7 ) Re 13 Settling Velocity and Drag Forces – Stokes’ Law V gD 2 ( part fluid ) 18 Ex. 8.2: 200 micron particle. How fast would it be falling and what would be the Reynolds number be? 2 200 V 6.05 10 5 m / s 2.42m / s 1 DV fluid (200 10 6 m)( 2.42m / s )(1.20kg / m 3 ) Re (1.8 10 5 kg / m s ) 32.3 0.3 14 Settling Velocity and Drag Forces – Particles too large for Stokes’ Law At large particle sizes, the flow of fluid around the sphere becomes turbulent. Ex. 8.3 shows that the settling velocity for 200 particle can be 50% of that calculated by Stokes’ law. Stokes’ law does not apply for particles much greater than 50-. For large particles (0.3 Re 1000) CD 24 (1 0.14 Re 0.7 ) Re 15 Settling Velocity and Drag Forces – Particles too small for Stokes’ Law 8MW RT Mean free path of gas molecules 0.499 P As d particle gas no longer looks like continuum, but rather like discrete particles. The particles may slip and reduce the drag force. CD CD C C Cunningham correction factor ' C =1+ A d particle A : a constant determined experiment ally, for specific particle fluid combinatio n 16 Settling Velocity 17 Settling Velocity and Drag Forces – Particles too small for Stokes’ Law Ex. 8-4: A 0.1- particle is settling in still air. What is its terminal settling velocity? V VStokes (1 A / D) At 1 atm and room temp, 0.07 Assume A 1.728 (derived for oil droplets) 1 A/D 1 1.728 (0.07/0.1) 2.21 V (6.05 10-7 )( 2.21) 1.34 10 6 m / s 18 Settling Velocity and Drag Forces – Stokes stopping distance Ex. 8-5: A 1- particle with SG =2 is ejected into air with V = 10 m/s. How far can it travel before it is stopped by viscous friction (ignore the gravity)? xStokes stopping Vo D 2 partC 18 (10)(10 6 ) 2 (2000)(1.12) 5 6 . 9 10 m 69 5 18(1.8 10 ) The value is very small. For particles of this size, air is a very viscous fluid. In the next chapter, we will see the Stokes stopping distance in a natural distance scale and they are related to control efficiencies. 19 Settling Velocity and Drag Forces – Aerodynamic particle diameter xStokes stopping Vo D 2 partC 18 Two particles have the same value of D2partC will have the same stopping distance for any initial velocity. Later will show that any two particles with the same value of this set will behave identically in several kinds of control devices – same aerodynamic behavior. 20 Settling Velocity and Drag Forces – Aerodynamic particle diameter Aerodynamic particle diameter for the particle in ex. 8.5: Da D partC D part 3 1/ 2 [( L)( M / L ) ] The symbol a stands for “microns, aerodynamic”. g g 0.5 Da 0.1 (2 3 )( 2.21) 0.21 ( 3 ) 0.21a cm cm 21 Settling Velocity and Drag Forces – Aerodynamic particle diameter (PE Sample Exam Question) The size and density of two particles are 10 & 1 g/cm3 and 5 & 4 g/cm3. The aerodynamic diameter (), respectively, of the particles are most nearly: (a) 10 and 20 (b) 10 and 10 (c) 10 and 5 (d) none of the above Da 10 (1) 10 a Da 5 (4) 10 a 22 Settling Velocity and Drag Forces – Diffusion of particles kTC D 3d p Note: D here is diffusivity Ex. 8.6: Estimate the diffusivity of a 1- particle in air at 20 oC and 1 atm. (1.38 10 23 kg m 2 / s 2 K )( 293)(1.16) D 3 (1.8 10 5 )(10 6 ) 2.8 10 11 m 2 / s Most gases diffuse in air with D of ~10-5 m2/s and D of solute in liquids are ~ 10-9 m2/s. Thus, particles on the order of a few microns do not diffuse rapidly. 23 PSD Function - Gaussian (normal) distribution variance standard deviation 2 250 200 n(ln(dp)) x xmean 2 d 1 exp 2 dx 2 2 cumulative fraction in the size range of interest 150 sigma=1.2 sigma=1.5 sigma=2.0 100 50 0 0.01 0.1 diameter (um) Plot d/dx vs. x symmetrical about xmean, the max occurs at x = xmean. It approaches zero asymptotically (bell-shape curve). A larger value of spreads the values over a wide range of x. 24 The area under the curve = 1. 1 PSD Function - Gaussian (normal) distribution No one has found a way to integrate the equation. The integration has been done numerically. Also a new variable, z (# of probits from the mean), is defined. z2 1 exp 2 2 cumulative fraction between 0 and x z number of standard deviations from the mean x xmean z= d dz 25 PSD Function - Gaussian (normal) distribution ‘Probability scale’ a scale linear in z (the values of corresponding to z are shown, instead. Gaussian distribution gives linear plot on normal vs. probability coordinates. Mean value is at z = 0 1 s = standard deviation xmean xi n 1 s [ ( xi xmean ) 2 ]1/ 2 n 1 As n becomes large, the s, sample standard deviation, becomes , or the (variance)0.5. 26 PSD Function – Lognormal distribution ln D ln Dmean 2 d 1 exp 2 d ln D 2 2 cumulative fraction for particles with diameter between 0 and D ln D ln Dmean z Many authors write the above equation with replaced by ln as ln D ln Dmean 2 d 1 exp 2 d ln D ln 2 2 (ln ) 27 PSD Function – Lognormal distribution Log-normal distribution gives linear plot on logarithmic vs. probability coordinates Mean value is at z = 0. Typical for PSD = 0.5 to 2, which corresponds to g, logarithmic standard deviation or geometric standard deviations, for the last equation (previous slide) of 1.64 to 7.39. The smallest possible value for g is 1.0, corresponding to a of zero. = ln(g) 1 Arithmetic mean diameter Di n 1 Log mean diameter exp( ln Di ) ( D1 D2 DN )1/ N 28 n PSD Function – Log-normal distribution How to get Dmean and from the line? Dmean = 20 From table, z =1 =0.8413 Z=1 =(x0.84 – xmean)/ = lnD0.84 – lnDmean = ln(70/20) = 1.25 g = exp1.25 =3.49 29 PSD Function – Log-normal distribution (PE Sample Exam Question) A log normally distributed particle mass has a geometric standard deviation g of 2.0 microns and a geometric mean diameter of 4 microns. A total of 84.1 of the particles are likely to have sizes (microns) less than (a) 2, (b) 4, (c) 6, (d) 8 ln g ln 2 ln( D84.1 / D50 ) D84.1 8 30 PSD Function – Distribution by weight and by number It is possible to define different mean diameters based on the type of cumulative fraction we use. if for D a is log normal, then for Db is log normal Db Da exp b a 2 V D3 A D 2 V D (Sauter) A N D 0 (Number) Say D3 20m (mass mean) and 1.25 D0 (20) exp 0 31.252 0.18m (number mean) For any particle size distribution, dnumber d Sauter darea dvolumemass 31 Types of Size Distributions Typical Rural distribution Typical Urban distribution # A V or M Volume and mass distributions are related by particle density (same shape!) Typically, environmental engineers are interested in mass 32 distributions. PSD Function Distribution function parameters (mean and standard deviation) are obtained by fitting the data They generally do a good job in the middle of the range. Beware of extrapolating beyond the data range (Ex. 8.8, predicts 6 men taller than 10 feet (3 m) in the United States based on height distribution statistics. For distribution functions having same (previous slide), we can compute Dmean, number, then draw a parallel line to find its distribution function. 33 Behavior of Particles in the Atmosphere The plot is for dby area/dD. If dby mass/dD was plotted the peak to the right would be larger. If dby number/dD were presented, then? 34 Behavior of Particles in the Atmosphere Finest (0.005 to 0.1): enter the atmosphere mostly by condensation of hot vapors from combustion. Midsize (0.1 to 1):formed by agglomeration of finer particles and by chemical conversion of gases and vapors to particles. They will then captured by drops in clouds (rainout) or by falling raindrops (washout). Larger (2 to 100): mechanically generated or industrial particle source – removed mainly by settling. 35 Behavior of Particles in the Atmosphere The first two peaks (last slide) are mainly secondary particles from gaseous precursors, SO2, NOx, NH3, & HC. NH3 is mainly from the biological sources. 36 The third peak is mainly primary particles.