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# Particle Technology Gas Cleaning

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The ninth lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics. The different mechanisms for the removal of dust from gases are covered and the design equations used for control, modelling and understanding of the equipment are presented and derived. Examples of industrial equipment for gas cleaning are included.

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### Particle Technology Gas Cleaning

1. 1. Gas Cleaning<br />Chapter 13 in Fundamentals<br />Watch this lecture at www.vimeo.com<br />Also visit; http://www.midlandit.co.uk/particletechnology.htm for further resources.<br />Course details: <br />Particle Technology, module code: CGB019 and CGB919, 2nd year of study.<br />Professor Richard Holdich<br />R.G.Holdich@Lboro.ac.uk<br />
2. 2. Gas Cleaning<br /><ul><li>Inertia
3. 3. Diffusional collection
4. 4. Target efficiency
5. 5. Material balance - e.g. fibrous filter
6. 6. Types of equipment</li></li></ul><li>Collection mechanisms<br />Diffusion<br />Inertia<br />Bounce<br />Sieving<br />Target collection efficiency<br />~0.1 to 1<br />Particle diameter, microns.<br />
7. 7. Dyson vacuum cleaner<br />The animated images shown above are reproduced by permission of Dyson Limited.<br />
8. 8. Inertia - rate of change of momentum<br />How long does it take to reach the terminal settling velocity (gas or liquid)?<br />Inertial collecting devices<br />Stokes’ law and STOKES NUMBER - note the difference!<br />
9. 9. Inertia - rate of change of momentum<br />Section 5.3<br />
10. 10. Force Balance<br />Apparent (buoyed) mass, drag & inertia:<br /><ul><li>Apparent mass is density x volume:</li></li></ul><li>Force Balance<br /><ul><li>Therefore:
11. 11. Where m is actual mass of particle - not buoyed mass.
12. 12. Validity depends on Stokes’ law being applicable.</li></li></ul><li>Force Balance<br />
13. 13. Acceleration & Inertia<br />Particles reach 99% of their terminal settling velocity very quickly.<br />Can use similar approach to characterise the inertia within a system.<br />Inertia can be used in gas cleaning systems.<br />
14. 14. Inertial collection<br />Gas streamlines/flow bend easily round target.<br />Flow<br />Target<br />Dust<br />Inertia carries heavier particles onto target - if they stick this is inertial collection.<br />
15. 15. Force Balance - Inertial Collection of Particles<br />Consider only drag & inertia:<br /><ul><li>mass is density x volume & rearranging:
16. 16. where: </li></li></ul><li>Force Balance - Inertial Collection of Particles<br /><ul><li>Make dimensionless as follows:</li></li></ul><li>Force Balance - Inertial Collection of Particles<br /><ul><li>The solution to the above equation is the same under all conditions so long as the parameters making up the term on the left may be allowed to vary individually but in such a way as to keep the overall value the same.</li></li></ul><li>Force Balance - Inertial Collection of Particles<br /><ul><li>Based on radius or diameter:</li></li></ul><li>Stop Distance<br /><ul><li>Integrating using Ug= 0 and Up=U0, at the start, provides the distance taken for a particle injected into still air to come to a halt - The Stop Distance.</li></li></ul><li>The Stokes Number<br /><ul><li>N.B. a dimensionless number and a measure of the SYSTEM inertia.
17. 17. It has both particle and collection device properties in its definition.
18. 18. Hint - high inertia given by terms on the top & vice versa for those underneath.</li></li></ul><li>The Stokes Number<br />= Stk =<br />Particle collectionefficiency<br />Stokes number<br />
19. 19. Collection mechanisms<br />Diffusion<br />Inertia<br />Bounce<br />Sieving<br />Target collection efficiency<br />~0.1 to 1<br />Particle diameter, microns.<br />
20. 20. Diffusional collection<br />Small particles move randomly across flow.<br />Flow<br />Target<br />Dust<br />Diffusion means that particles can be captured even behind the target.<br />
21. 21. Material Balance<br />Applicable to any device with a concentration gradient within the collection device. Example quoted is for a fibrous filter of the HEPA (high efficiency particulate air) type - this has a packing density of 2% (ish) fibres, 98% porosity.<br />
22. 22. Accumulation<br />-1<br />):<br />Accumulation is (SI units of kg s<br />Collection<br />Interstitial . Projected . Mass .<br /> concentration<br />efficiency<br />target area<br />velocity<br />of the dust<br />
23. 23. Projected target area<br />a<br />AdL<br />a<br />AdL<br />2<br />p<br />(<br />/<br />)<br />d<br />4<br />f<br />mass input - mass output = accumulation<br />volume of fibres in height dL is<br />The length of fibres in dL is<br /> fibre volume over fibre area, i.e.<br />
24. 24. Projected target area<br />a<br />AdL<br />4<br />p<br />d<br />f<br />a<br />AdL<br />2<br />p<br />(<br />/<br />)<br />d<br />4<br />f<br />Projected area to the gas flow is the product of<br />the length and diameter of the fibre<br />d<br />=<br />f<br />
25. 25. Accumulation<br />-1<br />):<br />Accumulation is (SI units of kg s<br />Collection<br />Interstitial . Projected . Mass .<br /> concentration<br />efficiency<br />target area<br />velocity<br />of the dust<br />U<br />a<br />AdL<br />4<br />g<br />r<br />h<br />.<br />.<br />.<br />C<br />s<br />s<br />-<br />a<br />p<br />d<br />1<br />f<br />
26. 26. Mass Balance<br />r<br />CU<br />A<br />g<br />s<br />¶<br />C<br />é<br />ù<br />+<br />r<br />CU<br />U<br />dL<br />A<br />ê<br />ú<br />g<br />g<br />s<br />¶<br />L<br />ë<br />û<br />-<br />r<br />U<br />dC<br />A<br />g<br />s<br />rate of dust input into layer is<br />rate of dust output from layer is<br />hence accumulation is<br />
27. 27. Mass Balance<br />U<br />a<br />AdL<br />4<br />g<br />r<br />h<br />.<br />.<br />.<br />C<br />s<br />s<br />-<br />a<br />p<br />d<br />1<br />f<br />accumulation<br />U<br />dC A<br />r<br />g<br />s<br />=<br />
28. 28. Mass Balance & Accumulation<br />é<br />ù<br />h<br />a<br />L<br />4<br />C<br />s<br />h<br />=<br />-<br />=<br />-<br />-<br />exp<br />1<br />1<br />ê<br />ú<br />p<br />a<br />-<br />C<br />d<br />(<br />)<br />1<br />ë<br />û<br />o<br />f<br />Hence,<br />dL<br />h<br />a<br />4<br />dC<br />s<br />-<br />=<br />-<br />p<br />a<br />C<br />d<br />(<br />)<br />1<br />f<br /> at<br />L=0<br /> to<br />C=C<br /> at<br />L=L<br />to give OVERALL<br />C=C<br />o<br />efficiency of<br />m<br />Single target efficiency minimum at approx 0.4<br />m.<br />
29. 29. In turbulent flow:<br />Critical trajectory within a boundary layer<br />Particle Collection Efficiency<br />
30. 30. Hence,<br /> and <br />Thus, equating the times<br />Particle Collection Efficiency<br />
31. 31. Model based on fraction particles removed = fraction volume particles are being removed from:<br />Particle Collection Efficiency<br />Negative sign as removal<br />
32. 32. Particle Collection Efficiency<br />Integrate over full length, and we want fractioncollected – not fraction remaining, hence:<br />Deutch Equation – forelectrostatic precipitators, where<br />Upis function of electric field<br />strength<br />
33. 33. Scrubber and Venturi Scrubber<br />Image located at http://en.wikipedia.org/wiki/File:Adjthroatplunger.jpg<br />
34. 34. Spray Tower Efficiency<br />
35. 35.
36. 36. Electrostatic Precipitator<br />
37. 37. Electrostatic Precipitator<br />Image located at http://www.arb.ca.gov/training/images/281.jpg<br />
38. 38. Electrostatic Precipitator<br />Image removed for copyright reasons.<br />For a suitable example see <br />http://www.alentecinc.com/company_profile.htm#Electrostatic%20precipitation. <br />
39. 39. Equipment Combined - Flowsheet<br />Image located at http://www.tfhrc.gov/hnr20/recycle/waste/images/cfa.gif<br />
40. 40. Industrial SME<br />NotesThe gas cyclone uses INERTIAL collection of dust whereas the hydrocyclone uses a centrifugal field force - it operates in a much higher viscosity medium. The two have very different operating principles.<br />